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Complete Unit 5

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Table of Contents

Unit 5 Pacing Chart -------------------------------------------------------------------------------------------- 1

Algebra 1 Unit 5 Skills List ---------------------------------------------------------------------------------------- 3

Unit 5 Lesson Plans -------------------------------------------------------------------------------------------- 4

Day 66 Bellringer -------------------------------------------------------------------------------------------- 20

Day 66 Activity -------------------------------------------------------------------------------------------- 22

Day 66 Practice -------------------------------------------------------------------------------------------- 25

Day 66 Exit Slip -------------------------------------------------------------------------------------------- 28

Day 67 Bellringer -------------------------------------------------------------------------------------------- 30

Day 67 Practice -------------------------------------------------------------------------------------------- 32

Day 67 Exit Slip -------------------------------------------------------------------------------------------- 34

Day 68 Bellringer -------------------------------------------------------------------------------------------- 36

Day 68 Activity -------------------------------------------------------------------------------------------- 38

Day 68 Practice -------------------------------------------------------------------------------------------- 43

Day 68 Exit Slip -------------------------------------------------------------------------------------------- 45

Day 69 Bellringer -------------------------------------------------------------------------------------------- 47

Day 69 Practice -------------------------------------------------------------------------------------------- 49

Week 14 Assessment -------------------------------------------------------------------------------------------- 53

Day 71 Bellringer -------------------------------------------------------------------------------------------- 58

Day 71 Activity -------------------------------------------------------------------------------------------- 60

Day 71 Practice -------------------------------------------------------------------------------------------- 62

Day 71 Exit Slip -------------------------------------------------------------------------------------------- 64

Day 72 Bellringer -------------------------------------------------------------------------------------------- 66

Day 72 Activity -------------------------------------------------------------------------------------------- 68

Day 72 Practice -------------------------------------------------------------------------------------------- 72

Day 72 Exit Slip -------------------------------------------------------------------------------------------- 79

Day 73 Bellringer -------------------------------------------------------------------------------------------- 81

Day 73 Activity -------------------------------------------------------------------------------------------- 83

Day 73 Practice -------------------------------------------------------------------------------------------- 86

Day 73 Exit Slip -------------------------------------------------------------------------------------------- 91

Day 74 Bellringer -------------------------------------------------------------------------------------------- 93

Day 74 Activity -------------------------------------------------------------------------------------------- 95

Day 74 Practice -------------------------------------------------------------------------------------------- 99

Day 74 Exit Slip -------------------------------------------------------------------------------------------- 109

Week 15 Assessment -------------------------------------------------------------------------------------------- 111

Unit 5 Test -------------------------------------------------------------------------------------------- 118

CCSS Algebra 1 Pacing Chart – Unit 5

HighSchoolMathTeachers © 2020 Page 1

Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements

5 – Linear Equations and Inequalities

14 – Literal Equations

66

CCSS.MATH.CONTENT.HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

The student will be able to solve and interpret the solution to multi-step linear equations and inequalities in context.

I can solve and interpret the solution to multi-step linear equations and inequalities in context.



67

CCSS.MATH.CONTENT.HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

The student will be able to write equations in equivalent forms to solve problems.

I can write equations in equivalent forms to solve problems.



68

CCSS.MATH.CONTENT.HSA.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

The student will be able to justify the steps in solving equations by applying and explaining the properties of equality.

I can justify the steps in solving equations by applying and explaining the properties of equality.



69

CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

The student will be able to extend to concepts used in solving numerical equations to rearranging formulas for a particular variable.

I can extend to concepts used in solving numerical equations to rearranging formulas for a particular variable.



70 Assessment Assessment Assessment Assessment

CCSS Algebra 1 Pacing Chart – Unit 5



15 – Inequalities

71

CCSS.MATH.CONTENT.HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

The student will be able to interpret the solution of an inequality in real terms.

I can interpret the solution of an inequality in real terms.


15 – Inequalities

72

CCSS.MATH.CONTENT.HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.


The student will be able to solve and interpret the solution to multi-step linear equations and inequalities in context.

I can solve and interpret the solution to multi-step linear equations and inequalities in context.


15 – Inequalities

73

CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.


The student will be able to graph the solution to linear inequalities in two variables

I can graph the solution to linear inequalities in two variables.


15 – Inequalities

74

CCSS.MATH.CONTENT.HSA.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.For example, represent inequalities describing

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

The student will be able to write and graph equations and inequalities representing constraints in contextual situations.

I can write and graph equations and inequalities representing constraints in contextual situations.


15 – Inequalities

75 Assessment Assessment Assessment Assessment

Algebra 1 Unit 5 Skills List


Algebra 1 Unit 5 Skills List

Number Unit Week CCSS Skill

25 5 14 A.REI.3 Solve advanced linear equations

26 5 14 A.REI.1

A.CED.4

Solve literal equations and justify the

steps

27 5 15 A.REI.3 Solve inequalities

28 5 15 A.REI.12 Graph inequalities

Unit 5 Lesson Plan

HighSchoolMathTeachers ©2020 Page 4

Unit 5 – Linear Equations and Inequalities

Course: Algebra 1

Topic: 14 – Literal Equations

Day: 66

Common Core State Standard: CCSS.MATH.CONTENT.HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Objective: The student will be able to solve and interpret the solution to multi-step linear equations and inequalities in context.

I can statement: I can solve and interpret the solution to multi-step linear equations and inequalities in context.

Procedures: 1. Students will complete the Week 14 Bellringer (Day 66). 2. Students will work with partners and complete the Day-66-Activity. 3. The Day 66 Presentation – Solving Word Problems with Variables on Both Sides will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-66-Exit-Slip before leaving for the day. 5. Use the Day 66 Practice as individual practice or homework.

Materials: Week 14 Bellringer (Day 66) Day 66 Activity Day 66 Presentation - Solving Word Problem with Variables on Both Sides Day 66 Practice Day 66 Exit Slip

Unit 5 Lesson Plan


Accommodations/Special Circumstances: Technology:

Reflection:

Extra/Additional Resources:

Unit 5 Lesson Plan



Course: Algebra 1


Day: 67

Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

Objective: The student will be able to write equations in equivalent forms to solve problems.

I can statement: I can write equations in equivalent forms to solve problems.

Procedures: 1. Students will complete the Week 14 Bellringer (Day 67). 2. Students will work with partners and complete the Day-67-Activity. 3. The Day 67 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-67-Exit-Slip before leaving for the day. 5. Use the Day 67 Practice as individual practice or homework.

Materials: Week 14 Bellringer (Day 67) Day 67 Activity Day 67 Presentation Day 67 Practice Day 67 Exit Slip

Accommodations/Special Circumstances:

Technology: http://express.smarttech.com/#

Unit 5 Lesson Plan


Reflection:


Unit 5 Lesson Plan



Course: Algebra 1


Day: 68

Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Objective: The student will be able to justify the steps in solving equations by applying and explaining the properties of equality.

I can statement: I can justify the steps in solving equations by applying and explaining the properties of equality.

Procedures: 1. Students will complete the Week 14 Bellringer (Day 68). 2. Students will work with partners and complete the A.REI.1 – Are they equivalent and A.REI.1 Equation MatchUp Practice. 3. The Day-68-Presentation-Multi-stepequations-with-tables-and-graphs-day-1 will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-68-Exit-Slip before leaving for the day. 5. Use the Day 68 Practice as individual practice or homework.

Materials: Week 14 Bellringer (Day 68) A.REI.1 – Are they equivalent A.REI.1 Equation MatchUp Practice Day 68 Presentation Day 68 Practice Day 68 Exit Slip

Unit 5 Lesson Plan


Accommodations/Special Circumstances: Technology:

Reflection:


Unit 5 Lesson Plan



Course: Algebra 1


Day: 69

Common Core State Standard: CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Mathematical Practice: CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Objective: The student will be able to extend to concepts used in solving numerical equations to rearranging formulas for a particular variable.

I can statement: I can extend to concepts used in solving numerical equations to rearranging formulas for a particular variable.

Procedures: 1. Students will complete the Week 14 Bellringer (Day 69). 2. Students will work with partners and complete the Day-69-Activity-Literal equations. 3. The Equivalent Equations (Notebook) will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-69-Exit-Slip before leaving for the day.

Materials: Week 14 Bellringer (Day 69) Day-69-Activity-Literal equations Equivalent Equations (Notebook) Day-69-Exit-Slip Day 69 Practice - Literal Equations

Unit 5 Lesson Plan


5. Use the Day 69 Practice – Literal Equations as individual practice or homework.


Technology: Online GeoBoard - http://www.mathlearningcenter.org/web-apps/geoboard

Reflection:


Unit 5 Lesson Plan



Course: Algebra 1

Topic: 15 – Inequalities

Day: 71

Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Objective: The student will be able to interpret the solution of an inequality in real terms.

I can statement: I can interpret the solution of an inequality in real terms.

Procedures: 1. Students will complete the Week 15 Bellringer (Day 71). 2. Students will work with partners and complete the Day 71 Notes and Day 71 Activity. 3. The Day 71 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-71-Exit-Slip before leaving for the day. 5. Use the Day 71 Practice, Day 71 Practice 2 or Day 71 Handout – Literal Equations as individual practice or homework.

Materials: Week 15 Bellringer (Day 71) Day 71 Activity Day 71 Notes Day 71 Presentation Day 71 Exit Slip Day 71 Practice Day 71 Practice 2 Day 71 Handout


Technology:

Unit 5 Lesson Plan


Reflection:


Unit 5 Lesson Plan



Course: Algebra 1


Day: 72

Common Core State Standard: CCSS.MATH.CONTENT.HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.


Objective: The student will be able to solve and interpret the solution to multi-step linear equations and inequalities in context.

I can statement: I can solve and interpret the solution to multi-step linear equations and inequalities in context.

Procedures: 1. Students will complete the Week 15 Bellringer (Day 72). 2. Students will work with partners and complete the Day 72 Activity. 3. The Day 72 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-72-Exit-Slip before leaving for the day. 5. Use the Day 72 Handout as individual practice or homework.

Materials: Week 15 Bellringer (Day 72) Day 72 Activity Day 72 Presentation Day 72 Exit Slip Day 72 Handout


Technology:

Unit 5 Lesson Plan


Reflection:


Unit 5 Lesson Plan



Course: Algebra 1


Day: 73

Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.


Objective: The student will be able to graph the solution to linear inequalities in two variables

I can statement: I can graph the solution to linear inequalities in two variables.

Procedures: 1. Students will complete the Week 15 Bellringer (Day 73). 2. Students will work with partners and complete the Day-73-Activity-Two variable equations. 3. The Day-73-Two variable inequalities will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-73-Exit-Slip before leaving for the day. 5. Use the Day 73 Handout as individual practice or homework.

Materials: Week 15 Bellringer (Day 73) Day-73-Activity-Two variable equations Day-73-Two variable inequalities Day 73 Exit Slip Day 73 Handout


Technology:

Unit 5 Lesson Plan


Reflection:


Unit 5 Lesson Plan



Course: Algebra 1


Day: 74

Common Core State Standard: CCSS.MATH.CONTENT.HSA.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.For example, represent inequalities describing

Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Objective: The student will be able to write and graph equations and inequalities representing constraints in contextual situations.

I can statement: I can write and graph equations and inequalities representing constraints in contextual situations.

Procedures: 1. Students will complete the Week 15 Bellringer (Day 74). 2. Students will work with partners and complete the Day-74-Activity-Inequalities problem solving. 3. The Day-74-Presentation-Inequalities problem solving will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-74-Exit-Slip before leaving for the day. 5. Use the Day-74-Practice – Inequalities problem solving as individual practice or homework.

Materials: Week 15 Bellringer (Day 74) Day-74-Activity-Inequalities problem solving Day-74-Presentation-Inequalities problem solving Day-74-Exit-Slip Day-74-Practice – Inequalities problem solving


Technology:

Unit 5 Lesson Plan


Reflection:


Day 66 Bellringer Name ____________________________________


Day 66

Solve the simple equations

1. 𝑥 − 7 = 15

2. 12 − 𝑦 = 5

3. 𝑠

2= 9

4. 4𝑏 = 20



Answer Key

Day 66

1. 𝑥 = 22 2. 𝑦 = 7 3. 𝑠 = 18 4. 𝑏 = 20

Day 66 Activity Name ____________________________________


Break-Even Point

The pep squad at Barton High School is selling pennants

to raise money for their activities. They must pay the

manufacturer $65.25 for the design of the pennant and

$2.15 for each pennant ordered.

The pep squad plans to sell each pennant for $4.50.

a) Write a verbal expression to describe the total amount paid to the manufacturer for the

pennants.

b) Revenue is the total amount received from the sales. Write a verbal expression to describe the

revenue from selling the pennants.

c) Copy and complete the table with amounts for cost and revenue from the given numbers of

pennant sales.

Number of Pennants 5 10 15 20 25 30

Total cost

Total revenue

d) Write an algebraic equation for the total cost in terms of the number of pennants, p, ordered.

e) Write an algebraic equation for the total revenue in terms of the number of pennants, p, sold.



f) The point at which the total revenue equals the total cost is the break-even point. Write an

equation that you could use to determine the number of pennants that must be sold to break

even.

g) Solve the equation You Wrote in Step 6. How many pennants need to be sold to break even? Be

sure that your answer is reasonable.

h) The profit from a sale is the total revenue minus the total cost. Write and solve an equation to

determine the number of pennants the pep squad must sell to make a profit of $100.



Answer Key

1. 65.25 plus $2.15 times the number of pennants purchased.

2. $4.50 times the number of pennants sold

3.

4. 𝐶 = 65.25 + 2.15𝑝

5. 𝑅 = 4.5𝑝

6. 65.25 + 2.15𝑝 ∗ 2.5

7. 28 pennants

8. 71 pennants

Number of Pennants 5 10 15 20 25 30

Total cost $76 $86.75 $94.50 $108.25 $119 $129.5

Total revenue $22.50 $45 $67.50 $90 $112.50 $135

Day 66 Practice Name ___________________________


1. Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per

minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for

the two containers to have the same amount of water?

2. Tim is choosing between two cell phone plans that offer the same amount of free minutes.

Cingular’s plan charges $39.99 per month with additional minutes costing $0.45. Verizon’s plan costs

$44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans

to cost the same?

3. The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster,

you must be a member. The Napster membership fee is $10. In addition, each purchased song costs

$0.89. How many downloaded songs, d, must be purchased for the monthly price of Napster to be the

same as iTunes?

4. Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B

has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the

two containers to have the same amount of water?

5. UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for

the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx

to cost the same?

6. A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches

every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the

same height? Let h represent the number of hours.

7. Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is

gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?



8. A full 355 mL can of Coke is leaking at a rate of 5 mL per minute into an empty can. How long

will it take for the two cans to have the same amount, a, of Coke?

9. On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled

is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you

spent the same amount each day, how many games, g, were bowled?

10. At one store a trophy costs $12.50. Engraving costs $0.40 per letter. At another store, the same

trophy costs $14.75. Engraving costs $0.25. How many letters, x12.5+.4x=14.75+.25x, must be engraved

for the costs to be the same?

11. You are looking for an apartment. There are two final choices. Apartment A has a $1000 security

deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many

months, m, will it take for the costs to be the same?

12. Lenny makes $55,000 and is getting annual raises of $2,500. Karl makes $62000, with annual

raises of $2,000. How many years, y, will it take for Lenny and Karl to make the same salary?

13. In 1987, 34.7 million households owned a dog, and 27.7 million owned a cat. Since then, dog

ownership has decreased by 0.025 million households per year, and cat ownership has increased by

0.375 million households per year. How many years, y, will it take for them to be equal?

14. In 2000, Ohio’s population was 11.4 million and increasing by 0.5 million each year. Michigan’s

population was 9.9 million, increasing by 0.6 million each year. When will the two states have the same

population? Let y represent the number of years.



Answer Key 1. 50 minutes

2. 100 minutes

3. 100 songs

4. 25 minutes

5. 20 pounds

6. 4 hours

7. 5 months

8. 35.5 minutes

9. 12 games

10. 15 letters

11. 20 months

12. 14 years

13. 17.5 years

14. Year 2015

Day 66 Exit Slip Name ___________________________


Container A has 500 L of water, and is being filled at a rate of 4 liters per minute.

Container B has 1000 L of water, and is being drained at 5 liters per minute. How

many minutes, m, will it take for the two containers to have the same amount of

water?



16. Answer Key 17. x=100 minutes

Day 67 Bellringer Name ___________________________


Day 67

Solve the equations

1. 𝑦

5 =

2

5

2. 17(𝑥 + 5) = 0

3. 2.5(𝑏 − 3.7) = 28.25

4. −24 = 7𝑥 + 18



Day 67

1. 𝑦 = 2 2. 𝑥 = −5 3. 𝑏 = 15 4. 𝑥 = −6

Day 67 Practice Name ____________________________________


Save each equation and justify each step.

1. 4𝑔 + 1 = 12 − 8𝑔

2. 1 − 3𝑥 = 2𝑥 + 8

3. 5 − 3𝑦 = 5𝑦 + 65

4. 4(2𝑤 + 5) = 12𝑤 − 9

5. 7𝑚 − 2(𝑚 − 3) = 3𝑚 − 14

6. 8𝑓 − 3(𝑓 + 6) = 2𝑓 − 16

7. 3𝑟 − 8 = 5𝑟 − 20

8. 15 − 2𝑦 = 12 − 8𝑦

9. 18 + 2𝑤 = 7𝑤 − 13

10. 5𝑥 − 7 = 2𝑥 + 2

11. 2(𝑦 − 3) + 4𝑦 + 8 = 3(𝑦 + 6)

12. 4𝑡 − 5 + 8𝑡 = 7(𝑡 + 6)



Answer Key

1. 11

12

2. −12

5

3. −71

2

4. 71

4

5. −10

6. 2

3

7. 6

8. −1

2

9. 61

5

10. 3

11. 51

3

12. 92

5



Which of the following equations are equivalent?

a.) 3𝑥 + 1 = 7𝑥 − 5

b.) 6𝑥 + 1 = 4𝑥 − 5

c.) 6𝑥 + 2 = 14𝑥 − 10

d.) 12𝑥 + 2 = 8𝑥 − 10

e.) 3𝑥 = 7𝑥 − 6

f.) 3𝑥 + 4 = 7𝑥 − 2

g.) 6𝑥 + 4 = 4𝑥 − 2

h.) 6𝑥 = 4𝑥 − 6

Explain your reasoning.



Answer Key

A, F, C, E are equivalent

B, D, G, H are equivalent

Explain Answers will vary, but should include the addition and multiplication

properties equality



Day 68

Solve the complex equations.

1. 4𝑥 + 7 − 6𝑥 = 5 − 4𝑥 + 4

2. 2(3𝑦 − 4) = 3𝑥 + 1

3. 5(2𝑧 + 3) = 3(4𝑧 + 1) − 2(3𝑧 + 2)

4. 𝑏

3+

1

2+

𝑏

4=

3

4+

𝑏

3



Answer Key

Day 68

1. 𝑥 = 1 2. 𝑦 = 3 3. 𝑧 = −4 4. 𝑏 = 1



Algebraic Properties and Proofs

You have solved algebraic equations for a couple years now, but now

it is time to justify the steps you have practiced. Remember taking action

without thinking is a dangerous habit!

The following is a list of the reasons one can give for each algebraic step one may take.

Complete the following algebraic proofs using the reasons above. If a step requires simplification by combining like terms, write simplify.

Given: 3𝑥 + 12 = 8𝑥 – 18

Prove: 𝑥 = 6

Statements

Reasons 1. 3x + 12 = 8x – 18 1. 2. 12 = 5x – 18 2. 3. 30 = 5x 3. 4. 6 = x 4. 5. x = 6 5.

ALGEBRAIC PROPERTIES OF EQUALITY ADDITION PROPERTY OF EQUALITY If a = b, then a + c = b + c

SUBTRACTION PROPERTY OF EQUALITY If a = b, then a – c = b – c

MULTIPLICATION PROPERTY OF EQUALITY If a = b, then a · c = b · c

DIVISION PROPERTY OF EQUALITY If a = b, then a

= b

c c

DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION or OVER SUBTRACTION

a(b + c) = ab + ac

a(b – c) = ab – ac SUBSTITUTION PROPERTY OF EQUALITY If a = b, then b can be substituted for

a in any equation or expression REFLEXIVE PROPERTY OF EQUALITY For any real number a, a = a SYMMETRIC PROPERTY OF EQUALITY If a = b, then b = a

TRANSITIVE PROPERTY OF EQUALITY If a = b and b = c, then a = c



Given: 3𝑘 + 5 = 17 Prove: 𝑘 = 4

Statements

Reasons 1. 3k + 5 = 17 1. 2. 3k = 12 2. 3. k = 4 3.

Given: −6𝑎 − 5 = −95

= −95 Prove: 𝑎 = 15

Statements

Reasons

Given: 3(5𝑥 + 1) = 13𝑥 + 5

Prove: 𝑥 = 1

Statements

Reasons



Given: 7𝑦 − 84 = 2𝑦 + 61

Prove: 𝑦 = 29

Statements

Reasons

Given: 4(5𝑛 + 7) − 3𝑛 = 3(4𝑛 − 9)

Prove: 𝑛 = −11

Statements

Reasons



Answer Key

Statements

Reasons 1. 3x + 12 = 8x – 18 1. Given 2. 12 = 5x – 18 2. Subtraction property of equality 3. 30 = 5x 3. Addition property of equality 4. 6 = x 4. Division property of equality 5. x = 6 5. Symmetric property of equality

Given: 3𝑘 + 5 = 17

Prove: 𝑘 = 4

Statements

Reasons 1. 3k + 5 = 17 1. Given 2. 3k = 12 2. Subtraction property of equality 3. k = 4 3. Division property of equality

Given: −6𝑎 − 5 = −95

= −95 Prove: 𝑎 = 15

Statements

Reasons 1. −6𝑎 − 5 = −95

2. −6𝑎 = −90

3. 𝑎 = 15

1. Given 2. Addition property of equality 3. Division property of equality



Given: 3(5𝑥 + 1) = 13𝑥 + 5

Prove: 𝑥 = 1

Statements

Reasons 1. 6(5𝑥 + 1) = 13𝑥 + 5 2. 15𝑥 + 3 = 13𝑥 + 5 3. 15𝑥 = 13𝑥 + 2 4. 2𝑥 = 2 5. 𝑥 = 1

1. Given 2. Distributive property of multiplication over addition 3. Subtraction property of equality 4. Subtraction property of equality 5. Division property of equality

Given: 7𝑦 − 84 = 2𝑦 + 61

Prove: 𝑦 = 29

Statements

Reasons 1. 7y − 84 = 2y + 61 2. 5y − 84 = 61 3. 5y = 145 4. y = 29

1. Given 2.Subtraction property of equality 3. Addition property of equality 4. Division property of equality

Given: 4(5𝑛 + 7) − 3𝑛 = 3(4𝑛 − 9)

Prove: 𝑛 = −11

Statements

Reasons 1. 4(5𝑛 + 7) − 3𝑛 = 3(4𝑛 − 9) 2. 20𝑛 + 28 − 3𝑛 = 12𝑛 − 27 3. 17𝑛 − 39 = 12𝑛 − 27 4. 5𝑛 + 28 = −27 5. 5𝑦 = −55 6. 𝑦 = −11

1. Given 2. Distributive property of multiplication 3. Subtraction 4. Subtraction property of equality 5. Subtraction property of equality 6. Division property of equality



Put the correct letter on the corresponding line below.

A. Area Model for Multiplication

B. Associative Property of Multiplication

C. Commutative Property of Multiplication

D. Property of Reciprocals Area Model for Multiplication

E. Multiplicative Identity Property of 1

F. Multiplication Property of Zero

G. Reciprocal of a Fraction Property

_____ 1. For any real number a, 𝑎 × 0 = 0 × 𝑎 = 0

_____ 2. Suppose a = 0 and b = 0. The reciprocal of 𝑎

𝑏 is

𝑏

𝑎 .

_____ 3. For any real number a, 𝑎 × 1 = 1 × 𝑎 = 𝑎.

_____ 4. Suppose a = 0. The reciprocal of a is 1

𝑎 .

_____ 5. For any real numbers a, b, and c, (𝑎𝑏)𝑐 = 𝑎(𝑏𝑐).

_____ 6. For any real numbers 𝑎 and b , 𝑎𝑏 = 𝑏𝑎.

_____ 7. The area 𝐴 of a rectangle with length l and width w is lw.



Answer Key

1. F 2. D 3. E 4. G 5. B 6. C 7. A



Identify the Properties of Mathematics

1) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 𝑎 𝑥(𝑏 + 𝑐) = 𝑎 𝑥 𝑏 + 𝑎 𝑥 𝑐

2) The sum of any number and zero is the original number. For example 𝑎 + 0 = 𝑎.

3) When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For examples (𝑎 𝑥 𝑏)𝑥 𝑐 = 𝑎 𝑥 (𝑏 𝑥 𝑐)

4) Adding 0 to and number leaves it unchanged. For example 𝑎 + 0 = 𝑎.

5) When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 𝑎 𝑥 𝑏 = 𝑏 𝑥 𝑎



Answer Key

1. Distributive Property 2. Identity Property of Addition 3. Associative Property of Multiplication 4. Addition Property of Zero 5. Commutative Property of Multiplication



Day 69

Solving problems involving unit conversions

1. Drew has a 1.2 meter long steel bar. He wants to cut it into 3 equal lengths. In millimeters, how long is should be?

2. Grace walks her dog 2 kilometers a day. In two days, how many meters does she and her dog walked?

3. A bag contains 4 boxes of chalk. A box of chalk is 2 kg in mass. How many grams are there in the bag?

4. Maya's weight is 75 kilograms, while Charlene's weight is 15 kilograms less than Selma. What is Charlene's weight in pounds?



Day 69

1. 400mm 2. 4000meters 3. 8000grams 4. 132.27lbs



Solve for the indicated variable in the parenthesis.

1) 𝑃 = 𝐼𝑅𝑇 (T) 2) 𝐴 = 2(𝐿 + 𝑊) (W)

3) 𝑦 = 5𝑥 − 6 (x) 4) 2𝑥 − 3𝑦 = 8 (y)

5) 𝑥+𝑦

3= 5 (x) 6) 𝑦 = 𝑚𝑥 + 𝑏 (b)

7) 𝑎𝑥 + 𝑏𝑦 = 𝑐 (y) 8) 𝐴 = 12⁄ ℎ(𝑏 + 𝑐) (b)

9) 𝑉 = 𝐿𝑊𝐻 (L) 10) 𝐴 = 4𝜋𝑟2 (r2)

11) 𝑉 = 𝜋𝑟2ℎ (h) 12) 7𝑥 − 𝑦 = 14 (x)

13) 𝐴 = 𝑥 + 𝑦

2 (y) 14) 𝑅 =

𝐸

𝐼 (I)

15) 𝑥 = 𝑦𝑧

6 (z) 16) 𝐴 =

𝑟

2𝐿 (L)

17) 𝐴 = 𝑎 + 𝑏 + 𝑐

3 (b) 18) 12𝑥 – 4𝑦 = 20 (y)

19) 𝑥 = 2𝑦 − 𝑧

4 (z) 20) 𝑃 =

𝑅 − 𝐶

𝑁 (R)



Answer Key

1) IR

PT 2)

2

2LAW

3)

5

6

yx 4)

3

28

xy

5) x = 15 – y 6) b = y – mx 7) b

axcy

8) c

h

Ab

2

9) WH

VL 10)

4

2 Ar 11)

2r

Vh

12)

7

14 yx

13) y = 2A – x 14) R

EI 15)

y

xz

6 16)

A

rL

2

17) b = 3A – a – c 18) y = 3x – 5 19) z = 2y – 4x 20) R = PN + C



Show your work:

Brandon knows that his truck route from Illinois to Tennessee is 430 miles long.

He also knows that Distance = 𝑟𝑎𝑡𝑒 ∗ 𝑡𝑖𝑚𝑒 (𝐷 = 𝑟𝑡)

How long will his route take if he averages a speed of 50 mi/hr.?

Start by first solving the formula for time. How long will his route take if he averages a speed of 50

mi/hr.?

Start by first solving the formula for time.



Answer Key

Solutions: Steps:

𝐷 = 𝑟𝑡 solve for 𝑡(𝑡𝑖𝑚𝑒)

𝐷

𝑟=

𝑟𝑡

𝑟

𝐷

𝑟= 𝑡

substitute 430 in for 𝐷 and 50 in for 𝑟 solve.

430

50= 8.6

It will take Brandon 8.6 hours.

53 Week 14 |

High School Math Teachers

Algebra 1

Weekly Assessment Package

Week 14

HighSchoolMathTeachers©2020

54 Week 14 |

Week 14

Weekly Assessments

55 Week 14 |

Week #14 1. Solve for x.

3x + (3x – 12) = 𝑥

4

2. Solve for x.

3𝑥 = 𝑎𝑥 + 5 + 𝑎

3. What is the greatest possible error for a

measurement of 5 inches?

4. The mean of the following data is 17. Find

the value of x.

14, 22, 8, 17, 15, x

5. Given the box and whisker graph, find the following.

Minimum: __________________ Maximum: __________________ Upper Quartile: ______________ Lower Quartile: ______________ Median: ____________________ 6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are

there in 3 acres?

56 Week 14 - KEYS |

Week 14 - KEYS

Weekly Assessments

57 Week 14 - KEYS |

Week #14 KEY

1. Solve for x.

3x + (3x – 12) = 𝑥

4

𝟔𝒙 − 𝟏𝟐 =𝒙

𝟒

𝐱 = 𝟐

2. Solve for x.

3𝑥 = 𝑎𝑥 + 5 + 𝑎

𝟑𝒙 − 𝒂𝒙 = 𝟓 + 𝒂

𝒙(𝟑 − 𝒂)

(𝟑 − 𝒂)=

𝟓 + 𝒂

𝟑 − 𝒂

𝒙 =𝟓 + 𝒂

𝟑 − 𝒂

3. What is the greatest possible error for a

measurement of 5 inches?

0.5 feet (The greatest possible error is half of the unit of measure to which a measure is rounded.)

4. The mean of the following data is 17. Find

the value of x.

14, 22, 8, 17, 15, x

𝟕𝟔 + 𝒙

𝟔= 𝟏𝟕

𝒙 = 𝟐𝟔

5. Given the box and whisker graph, find the following.

Minimum: ____2________ Maximum: ____16___________ Upper Quartile: ___11_________ Lower Quartile: ___4________ Median: ____6______________ 6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are

there in 3 acres?

𝟑 𝒂𝒄𝒓𝒆𝒔 ×𝟏 𝒎𝒊

𝟔𝟒𝟎 𝒂𝒄𝒓𝒆𝒔×

𝟓𝟐𝟖𝟎 𝒇𝒕

𝟏 𝒎𝒊×

𝟓𝟐𝟖𝟎 𝒇𝒕

𝟏 𝒎𝒊= 𝟏𝟑𝟎, 𝟔𝟖𝟎 𝒇𝒕𝟐



Day 71

Solve each literal equations for the indicated variable.

1. 7𝑏 − 𝑎 = 14 𝑓𝑜𝑟 (𝑏)

2. 𝑧 =𝑥+𝑦

2 𝑓𝑜𝑟 (𝑦)

3. 𝑎 = 𝑥+𝑦+𝑧

3 𝑓𝑜𝑟 (𝑦)

4. 2𝑗 − 3𝑐 = 9 𝑓𝑜𝑟 (𝑐)



Answer Keys

Day 71

1. 𝑏 =14+𝑎

7

2. 𝑦 = 2𝑧 − 𝑥

3. 𝑦 = 3𝑎 − 𝑥 − 𝑧

4. 𝑐 =9−2𝑗

−3

Day 71 Activity Name ___________________________


An advertising agency is interested in knowing the effectiveness of its campaign for Fiesta Foods, Inc. this

year. The change in sales since the campaign began may show the effectiveness of the campaign. The

annual sales amount for the year before the new campaign was started is shown on this number line.

1. What is the dollar amount of last year's sales?

2. Lower annual sales this year than last year may show that the advertising campaign is not very effective.

Name an amount less than last year's sales.

3. Name an amount greater than last year's sales.

4. In Question 2, could you have named other lesser amounts? How many others? Where are the points

corresponding to these amounts located on the number line above?

5. In Question 3, could you have named other greater amounts? How many others? Where are the points

corresponding to these amounts located on the number line above?

6. Can you name an amount that is not less than, not greater than, and not equal to last year's sales?

Day 71 Activity Name ___________________________


Answer Key

1. The amount of last year’s sales is $1,000,000.

2. An amount less than last year’s sales is $500,000. (Answers will vary)

3. An amount greater than last year’s sales is $2,000,000. (Answers will vary)

4. Yes, we could name an infinite number of lesser amounts. These points are located left of the last

year’s sales.

5. Yes, we could name an infinite number of greater amounts. These points are located right of the

last year’s sales.

6. No, we cannot. Each value is either less than or greater than or equal to last year’s sales.

Day 71 Practice Name __________________________


Solve the following inequalities and graph the solution sets on the number lines.

Please show work.

1. 𝑥 − 4 > 1

2. 𝑥 + 1 ≤ 4

3. 4𝑦 ≥ 8

4. −5𝑤 < 10

5. 4𝑥 > −28

6. 27 > −9𝑦

7. 2𝑦 + 7 < 17

8. 2(2𝑥 − 8) − 8𝑥 ≤ 0

9. 5𝑥 + 4 ≤ 11 − 2𝑥

10. 5𝑥 − (𝑥 − 8) > 9 + 3(2𝑥 − 3)

Day 71 Practice Name __________________________


Answer Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.



The sum of three consecutive numbers is 72.

What are the smallest of these numbers?



Answer Key

23



Day 72 Solve these one-variable inequalities.

1. 3 + 𝑥 > 2

2. −7𝑥 > 14

3. 2𝑥 + 3 > 13

4. 12𝑥 − 6𝑥 ≤ 48



Answer Key

Day 72

1. 𝑥 > −1 2. 𝑥 < −2 3. 𝑥 > 5 4. 𝑥 ≤ 8



You can compare an equation and an inequality, such as 𝑥 = 8 and 𝑥 < 8, in another way. Recall that

adding the same number to both sides of an equation produces an equivalent equation. So does

subtracting the same number from both sides and multiplying or dividing both sides by the same

number. Find out if these operations produce inequalities that remain true.

One solution of the inequality 𝑥 < 8 is 7, because 7 < 8, as shown on this number line.

The number line below shows the result of adding 3 to both sides of the inequality 7 < 8. Because 10 is

to the left of 11, you can see that 10 < 11.

1. Selecting a different positive and negative integer, you and your partner should each

a. add the positive integer to both sides of 7 < 8

b. add the negative integer to both sides of 7 < 8

c. subtract the positive integer from both sides

d. subtract the negative integer from both sides

e. multiply both sides of 7 < 8 by the positive integer

f. multiply both sides by the negative integer

g. divide both sides by the positive integer

h. divide both sides by the negative integer

2. Use a number line to help you decide whether each new inequality is true or not. Record your results in a table like this.

New Inequality resulting from

True or not true?

Partner A Partner B

Adding positive integer

Adding negative integer

Subtracting positive integer

7 + 3 < 8 + 3

10 < 11 𝑡𝑟𝑢𝑒



3. What operations resulted in untrue inequalities?

4. Change the inequality symbol to make each untrue inequality true

5. Substitute a negative solution for 𝑥 in 𝑥 < 8. Repeat Activities 1 - 2 using this inequality.

6. Substitute a value for 𝑥 in 𝑥 > −3 that results in a true inequality. Repeat Activities 1 - 2.

In the following inequalities, 𝑎 and 𝑏 are real numbers, 𝑐 is a positive real number (𝑐 > 0), and 𝑑 is a

negative real number (𝑑 < 0). Based on your findings in Activities 1-6, tell whether each statement is

true or false.

7. 𝑖𝑓 𝑎 < 𝑏, 𝑡ℎ𝑒𝑛 𝑎 – 𝑐 < 𝑏 – 𝑐.

8. 𝑖𝑓 𝑎 > 𝑏, 𝑡ℎ𝑒𝑛 𝑎

𝑐 <

𝑏

𝑐.

9. 𝑖𝑓 𝑎 < 𝑏, 𝑡ℎ𝑒𝑛 𝑎 – 𝑑 > 𝑏 – 𝑑.

10. 𝑖𝑓 𝑎 > 𝑏, 𝑡ℎ𝑒𝑛 𝑎𝑑 < 𝑏𝑑.

11. 𝑖𝑓 𝑎 < 𝑏, 𝑡ℎ𝑒𝑛 𝑎𝑐 > 𝑏𝑐.



Replace with the inequality symbol that makes each statement.

12. 𝑖𝑓 𝑥 < 8, 𝑡ℎ𝑒𝑛 𝑥 + 10 8 + 10.

13. 𝑖𝑓 – 𝑥 > 2 , 𝑡ℎ𝑒𝑛 (−1)(−𝑥) (−1)(2).

14. 𝑖𝑓 𝑥 – 6 ≤ − 4, 𝑡ℎ𝑒𝑛 𝑥 – 6 + 6 − 4 + 6.

15. 𝑖𝑓 𝑥 + 5 < −1, 𝑡ℎ𝑒𝑛 𝑥 + 5 − 5− 1 − 5

16. 𝑖𝑓3

4 𝑥 ≥ −24, 𝑡ℎ𝑒𝑛

4

3

3

4 𝑥

4

3 (−24).

17. 𝑖𝑓 –2

3 𝑥 ≥ 18, 𝑡ℎ𝑒𝑛 (−

3

2) (−

2

3𝑥) (−

3

2)(18).

18. 𝑖𝑓 − 15𝑥 < 30, 𝑡ℎ𝑒𝑛 −15𝑥

−15

30

−15.



ANSWER KEY

1. Answer will vary 2. Answer will vary 3. Multiplying of dividing by a negative number resulted in untrue inequalities 4. Answer will vary 5. Answer will vary 6. Answer will vary 7. True 8. False 9. False 10. True 11. False 12. < 13. < 14. ≤ 15. < 16. ≥ 17. ≤ 18. >



1. Which is the solution to the following inequality?

2𝑥 − 7 ≥ 9

a. 𝑥 ≥ 8

b. 𝑥 ≥ 1

c. 𝑥 ≤ 8

d. 𝑥 ≥ −1

2. What is the solution to the inequality below?

12𝑥 > 5(𝑥 − 2)

a. 𝑥 > −2

7

b. 𝑥 < −2

7

c. 𝑥 > −10

7

d. 𝑥 < −10

7

3. Which of the following numbers is a solution for the inequality shown below?

7(2𝑥 − 3) > 49

a. 10

b. 5

c. 0

d. -6



4. Which of the following defines the solution set for the inequality shown below?

−2𝑥 + 3 ≥ 6

a. 𝑥 ≥ −9

2

b. 𝑥 ≤ −9

2

c. 𝑥 ≥ −3

2

d. 𝑥 ≤ −3

2

5. Which number is closest to the median of the data set represented by the box-and whiskers plot

below?

a. 75

b. 65

c. 60

d. 50



6. The following is an ordered list of monthly normal high temperatures for Phoenix, AZ.

66, 66, 70, 74, 75, 84, 88, 93, 99, 103, 103, 105

Which box-and-whisker plot best displays the data?



7. Which of these lines has a slope of −3?



8. What are the y-intercept and the slope of the graph below?

9. Ms. Cook's class bought 2 bags of concrete and some bricks to build a border for their class garden. The

bricks cost $51. The total cost of the bricks and the concrete was $57. Which equations can be used to nd

the cost,b, of 1 bag of concrete?



10. Look at the table of values.

x y

-1 -4

0 -1

1 2

2 5

3 8

Which equation represents the relationship between x and y?



Answer Key

1.

2𝑥 − 7 ≥ 9 2𝑥 ≥ 9 + 7

2𝑥 ≥ 16

𝑥 ≥16

2

𝑥 ≥ 8

Correct answer: a.

2.

12𝑥 > 5(𝑥 − 2)

12𝑥 > 5𝑥 − 10

12𝑥 − 5𝑥 > −10

7𝑥 > −10

𝑥 > −10

7

Correct answer: c.

3.

7(2𝑥 − 3) > 49

14𝑥 − 21 > 49

14𝑥 > 49 + 21

14𝑥 > 70

𝑥 >70

14

𝑥 > 5

Correct answer: a.

4.

−2𝑥 + 3 ≥ 6

−2𝑥 ≥ 6 − 3

−2𝑥 ≥ 3

𝑥 ≤ −3

2

Correct answer: d.

5.

Correct answer: b.

6.

Correct answer: D

7.

Correct answer: D

8.

Correct answer: C

9.

Correct answer: C

10.

Correct answer: D



Graph the inequality −3(𝑥 − 2) ≤ 12.



Answer Key



Day 73

Graph these one-variable inequalities

1. 𝒙 ≤ 𝟕

2. – 𝟓 > 𝑥

3. 𝒙 > 3

4. −𝒙 ≥ 𝟐



Answer Key

Day 73

𝟏.

2.

3.

4.



Consider a situation where a teacher has 4 pieces of candies to give to two students. Let the

names of the students be Jaylen and Jaslene. Either one of them can get all the pieces of

candies or get nothing.

1. Write all possible combination of the number of candies that they can get

2. Taking the combination as the coordinates of points, plot the points and draw a line through

them, taking Jaylen and Jaslene to be 𝑥 and 𝑦 respectively.



3. Identify the wanted solution by shading the region where there are no solutions.

4. Name any other inequalities that apply to this situation.

5. Write all the inequalities definition the wanted region.



Answer Keys Day 73:

1. (0,4), (1,3), (2,2), (3,1) and (4,0)

2.

3.

4. 𝑥 ≥ 0, 𝑦 ≥ 0

5. 𝑥 ≥ 0, 𝑦 ≥ 0 and 𝑦 + 𝑥 ≤ 4



Will the Spurs Win? Guided Activity

The Spurs are facing the Mavericks in the second round of the NBA playoffs. It’s the start of the 4th quarter

and the Spurs are down 56 to 74!

1. Write an inequality to represent combinations of 2-point and 3-point shots needed for the Spurs to

score at least 18 points. Use x to represent the number of 2-point shots and y to represent the number of

3-point shots.

2. Select different combinations of 2-point and 3-point shots to test. Use the values to complete the table.

x y Number of points scored Win, Lose or Tie?



3. Plot the points on the grid. Use a GREEN color to plot points when the Spurs win and a RED color to plot

points when the Spurs lose.

4. Identify two points on the “boundary line” that separates situations where the Spurs win and when

they lose. What do these points represent?

5. Shade in our desired region. (The side when the Spurs would win.) What does every point in this region

represent?



6. Use these points to develop a slope-intercept form of the line.

7. How could we have arrived at this equation using the inequality from #1? Write your own step-by-step

system for graphing a single linear inequality.



Answer Key

1. 2𝑥 + 3𝑦 ≥ 18

2.

x y Number of points scored Win, Lose or Tie?

0 0 0 Lose

1 1 5 Lose

2 2 10 Lose

3 3 15 Lose

4 4 20 Win

5 5 25 Win

6 6 30 Win

3 4 18 Tie

6 2 18 Tie

3.

4. Example: (3,4)and (6,2)

The points represent the combination of shots that results in a tie.



5.

Every point in this region represent the case when the Spurs would win.

6. 𝑦 = (−2/3)𝑥 + 6

7. 2𝑥 + 3𝑦 ≥ 18

3𝑦 ≥ 18 − 2𝑥

3𝑦 ≥ −2𝑥 + 18

𝑦 ≥ −2

3𝑥 + 6



Graph 𝑦 ≤ 2𝑥 − 4



Answer Key



Day 74 Graph the following two-variable inequalities.

1. 𝟐𝒙 + 𝟑𝒚 ≥ 𝟒𝟓

2. 𝟒𝒙 − 𝟒𝒚 ≤ 𝟏𝟔

3. 𝟐(𝒙 + 𝒚) ≤ −𝟏𝟎

4. – 𝟑(𝒙 − 𝟕𝒚) ≥ −𝟐𝟏



Answer Key

Day 74

1.

2.

3.

4.


HighSchoolMathTeachers©2020 Page 95

Gammy, a businessman, has $5000 to invest in two different accounts A and B, in multiples of

$1000. Each account must get at least $1000. Gammy earns interest of $600 from A and $550

from B on every $1000 saved.

1. List all possible savings plans as ordered pairs:

(amount invested in account A, amount invested in account B)

2. Taking the ordered pairs of the saving plans as coordinates of points, draw the line through

the points representing the saving plans. Use a scale of 1: 1000.



3. Identify any constraints on accounts A or B.

4. Draw a graph showing the region representing savings plans that meet the requirements.

5. Write down all the inequalities involved.

6. Determine the best saving plan.



Answer Keys Day 74:

1. ($1000, $4000), ($2000, $3000), ($3000, $2000) and ($4000, $1000)

2.

3. 𝐴 ≥ $1000, 𝐵 ≥ $1000



4.

5. 𝐴 ≥ $1000, 𝐵 ≥ $1000

𝐴 + 𝐵 ≤ $5000

6. Integer values are(4,1), save $4000 in A and $1000 in B to get a maximum of $2950.



Use the information below to answer questions 1 – 5.

Millen wants to buy laptops and printers for his new company. The cost of one laptop is $700

while that of a printer is $200. He has a budget of $6000.

1. Write two basic one-variable inequalities defining the constraints on the problem.

2. Write a two-variable inequality representing the problem.

3. Draw the inequalities on an 𝑥 − 𝑦 plane, shading the unwanted region.



4. Find the number of printers and laptops to serve at least 4 people while maximizing the

budget.

5. Determine the total amount spent on the purchase of the items.

Use the following information to answer questions 6 – 10

A soccer federation is planning to make total sales of $81,000 during the forthcoming indoor

games. The cost of a ticket is $35 for adults and $20 for children. The Federation wants to know

the number of people that should buy the tickets to reach the target.

6. Write two basic one-variable inequalities defining the constraints of the problem.





9. Find the number of adults ticket sales needed to meet the goal if 600 child tickets are sold.

10. Determine the total amount collected for the ticket sales described in question 9.



Use the following information to answer questions 11-16.

Hein has two dogs, Jerry and Topy. Topy consumes 14 pounds of food per month while Jerry

consumes 20 pounds of food per month. Hein bought 100 pounds of food costing $13 per

pound. He wants to know the most economical way to distribute the food to the dogs.

11. Write two basic one-variable inequalities defining the constraints of the problem.





14. Hein decides that each dog needs to eat from the purchased food for at least 2 months. How many whole months should each dog be fed from the purchased from in order to use as much as possible? 15. Determine the total quantity of food consumed given the answers provided for question 14.

16. Determine the cost of the food consumed in question 15.

Use the following information to answer questions 17 – 20

A soccer club is planning to construct a soccer stadium that will hold 20,000. To maximize the

revenue they decided to allocate 5000 higher-priced VIP seats and save the rest for other

occupants. They would like to set optimal ticket prices for both VIP and non-VIP tickets. Each

type of ticket needs to cost at least $100. In addition, to maintain the balance between the

types of tickets, the revenue should not be more than $3,600,000 per game.

17. What is the number of seats set aside for other occupants?

18. Write two one-variable inequalities modeling the constraints of the problem.



19. Write two two-variable inequalities modeling the problem.

20. Draw the inequalities and identify the region satisfying all the inequalities



Answer Keys Day 74:

1. 𝑥 > 0, 𝑦 > 0 2. 7𝑥 + 2𝑦 ≤ 60 3.

4. Any of these 6 laptops and 9 printers 4 laptops and 16 printers

5. $6000

6. 𝑥 > 0, 𝑦 > 0

7. 35𝑥 + 20𝑦 ≥ 81000



8.

9. 3000

10. $81,000

11. 𝑥 > 0, 𝑦 > 0

12. 14𝑥 + 20𝑦 ≤ 1000



13.

14. 4 months for Topy and 2 months for Jerry

15. 96 pounds

16. $1248

17. 15000 seats

18. 𝑥 > 0, 𝑦 > 0

19. 𝑥 + 𝑦 ≥ 100, 5000𝑥 + 15000𝑦 ≤ 3,600,000



20.

Day 74 Exit Slip Name ____________________________________


Find the Error

Reiko and Kristin are solving 4𝑦 ≤8

3𝑥 by graphing. Is either of them correct? Explain your reasoning

Day 74 Exit Slip Name ____________________________________


Answer Key

Reiko is correct. Kristin made the mistake of checking a point on the line.

112

Week 15

Weekly Assessments

113

Week #15 1. Solve and graph the inequality.

6𝑥 + 5 < 10 − 2𝑥

2. Your test scores for your history class so

far were 74%, 82%, 76%, 75%, and 80%.

On the last test of the year, you studied

hard and earned a 100%. How did this

change your test average?

3. Solve for x.

𝑥 + 1

3= 4𝑥 − 7

4. The formula 𝑃 =𝐹

𝐴 gives the pressure P for

a force F and an area A. Solve this formula

for A.

5. Six ninth-grade students and six 12th-grade students were asked: How many movies have

you seen this month? Here are their responses.

Ninth-grade students: 5, 1, 2, 5, 3, 8 12th-grade students: 4, 2, 0, 2, 3, 1

a. How does the mean compare for each of these data sets?

114

6. Identify the outlier in the data below. Find the mean of the speed of the animals with and

without the outlier. How does the outlier change the mean?

Animal Speed (MPH)

Peregrine Falcon 200 + Cheetah 70

Lion 50 Wildebeest 50

Elk 45 Ostrich 40 Rabbit 35

How does the outlier change the mean?

Outlier: ____________________________________

Mean Speed with Outlier: _________________

Mean Speed without Outlier: ______________

115

Week 15 - KEYS

Weekly Assessments

116

Week #15 KEY 1. Solve and graph the inequality.

6𝑥 + 5 < 10 − 2𝑥

𝑥 < 5/8

5/8

2. Your test scores for your history class so

far were 74%, 82%, 76%, 75%, and 80%.

On the last test of the year, you studied

hard and earned a 100%. How did this

change your test average?

Average 1: 𝟑𝟖𝟕

𝟓≈ 𝟕𝟕. 𝟒

Average 2: 𝟒𝟖𝟕

𝟔≈ 𝟖𝟏. 𝟐

The test average increased by ≈ 3.8 points.

3. Solve for x.

𝑥 + 1

3= 4𝑥 − 7

𝒙 + 𝟏 = 𝟏𝟐𝒙 − 𝟐𝟏

𝒙 = 𝟐

4. The formula 𝑃 =𝐹

𝐴 gives the pressure P for

a force F and an area A. Solve this formula

for A.

𝑷𝑨 = 𝑭

𝑨 =𝑭

𝑷

5. Six ninth-grade students and six 12th-grade students were asked: How many movies have

you seen this month? Here are their responses.

Ninth-grade students: 5, 1, 2, 5, 3, 8 12th-grade students: 4, 2, 0, 2, 3, 1

a. How does the mean compare for each of these data sets?

Ninth graders: 𝟐𝟒

𝟔= 𝟒

12th grade students: 𝟏𝟐

𝟔= 𝟐

The ninth grade students, on average, saw two more movies last month than the 12th graders.

117

6. Identify the outlier in the data below. Find the mean of the speed of the animals with and

without the outlier. How does the outlier change the mean?

Animal Speed (MPH)

Peregrine Falcon 200 +

Cheetah 70 Lion 50

Wildebeest 50

Elk 45 Ostrich 40

Rabbit 35 How does the outlier change the mean? The outlier increased the mean by 21.7 MPH.

Outlier: ____Peregrine Falcon____________

Mean Speed with Outlier: __70_________

Mean Speed without Outlier: ___48.3_________

Unit 5 Test Name ____________________________


1. The choir at the High School is selling t-shirts to raise money for their activities. They must pay the manufacturer $85.75 for the design of the t-shirt and $4.00 for each t-shirt ordered. The choir plans to sell each t-shirt for $10.00.

a) Write a verbal expression to describe the total amount paid to the manufacturer for

the t-shirts. b) Write an algebraic expression for the total cost in terms of the number of t-shirts, x,

ordered. c) Write an algebraic expression for the total revenue in terms of the number of t-shirts,

x, sold. d) The point at which the total revenue equals the total cost is the break-even point.

Write an equation that you could use to determine the number of t-shirts that must be sold to break even.

2. Complete the following algebraic proof. The chart of Algebraic Properties

of Equality needs to be included here. (You can find it on Week 14, Day 68 Activity (p.22). If a step requires simplification by combining like terms, write simplify.

Given: 2𝑥 + 8 = 6𝑥 – 16

Prove: 𝑥 = 6

Statements Reasons

1. 2𝑥 + 8 = 6𝑥 – 16 1.

2. 8 = 4x – 16 2.

3. 24 = 4x 3.

4. 6 = x 4.

5. x = 6 5.

Unit 5 Test Name ____________________________


Solve each equation for the variable indicated in the parenthesis.

3. 𝑃 = 𝐼𝑅𝑇 (R)

4. 𝐴 = 2(𝐿 + 𝑊) (L)

5. 𝑦 = 3𝑥 − 1 (x)

6. 3𝑥 − 4𝑦 = 8 (y)

7. Match the each equation in column 1 with an equivalent equation in column 2:

i.) 3𝑥 + 1 = 7𝑥 − 5

j.) 6𝑥 − 2 = 4𝑥 + 1

k.) 6𝑥 + 2 = 14𝑥 − 8

l.) 12𝑥 + 2 = 8𝑥 − 10

m.) 3𝑥 = 7𝑥 − 6

n.) 3𝑥 + 1 = 7𝑥 − 4

o.) 6𝑥 + 1 = 4𝑥 − 5

p.) 6𝑥 + 1 = 4𝑥 + 4

Unit 5 Test Name ____________________________


Solve the following inequalities and graph the solution sets on the number lines.

Please show work.

8. 𝑥 − 6 > 1

9. 𝑥 + 3 ≤ 4

10. 4𝑦 ≥ 12

11. −10𝑤 < 10

12. 5𝑤 < −20

Replace with the inequality symbol that makes each statement true.

13. 𝑖𝑓 𝑥 < 5, 𝑡ℎ𝑒𝑛 𝑥 + 10 5 + 10.

14. 𝑖𝑓 – 𝑥 > 6 , 𝑡ℎ𝑒𝑛 (−1)(−𝑥) (−1)(6).

15. 𝑖𝑓 𝑥 – 2 ≤ − 3, 𝑡ℎ𝑒𝑛 𝑥 – 2 + 2 − 3 + 2.

16. 𝑖𝑓 𝑥 + 5 < −3, 𝑡ℎ𝑒𝑛 𝑥 + 5 − 5− 3 − 5

Unit 5 Test Name ____________________________


Graph each of the following inequalities.

17. 𝑦 ≥ −𝑥

18. 𝑦 ≤ −2

5𝑥 + 5

19. 𝑦 ≥1

3𝑥 − 2

20. 𝑦 >2

3𝑥 + 7

Unit 5 Test Name ____________________________


Answer Key 1. a. the total will be the design cost of $85.75 in addition to the cost per shirt of

$4.00 each. b. 85.75 + 4𝑥 c. 10𝑥 d. 10𝑥 = 85.75 + 4𝑥

2.

3. 𝑅 =𝑃

𝐼 𝑇

4. 𝐿 =𝐴

2− 𝑊

5. 𝑥 =𝑦+1

3

6. 𝑦 =3𝑥−8

4 𝑜𝑟 𝑦 =

3

4𝑥 − 2

Match the equivalent equations.

7. a.) e.

b) h.

c) f.

d) g

8. 𝑥 > 7

9. 𝑥 ≤ 1

Statements Reasons

1. 2𝑥 + 8 = 6𝑥 – 16 1. Given

2. 8 = 4x – 16 2. Subtraction property of equality

3. 24 = 4x 3. Addition property of equality

4. 6 = x 4. Division property of equality

5. x = 6 5. Reflexive property.

Unit 5 Test Name ____________________________


10. 𝑦 ≥ 3

11. 𝑤 > −1

12. 𝑤 < −4

13. <

14. <

15. ≤

16. <

17.

18.

19.

20.

algebra 1 complete unit 5 - high school math teachers · unit week day ccss standards mathematical...

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