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CHAPTER 7

Solving Equations and Inequalities

Chapter 7:

Solving Equations & Inequalities

� 7.2 - Solving Two-Step Equations

� 7.4 - Circles and Circumferences

�QUIZ 7A: on 7.2 and 7.4 ���� Friday 3/15

� 7.5 - Solving Equations with Variables of Each Side

� 7.6 - Solving Multi-Step Inequalities

� 7.7 - Writing Inequalities

�QUIZ 7B: on 7.5 - 7.7 ���� Friday 3/22

� 7.8 - Using the Metric System

� TEST on Chapter 7���� BLOCK 3/27 and 3/28

Chapter 7.2 Solving Two-Step Equations

� Objective:

� To solve equations that involve more than one operation

� Warm-Up:

� P326 (1-10 ALL)

Chapter 7.2 Solving Two-Step Equations

� Notes:

� Let’s Review…What’s an equation?

“Peal the onion” or Work outside ���� in.

1. c – 19 = 17

2. -3n + 8 = -7

3. 2 + 4m = 1

4. 3 = n - 3

4

Chapter 7.2 Solving Two-Step Equations

� Your turn…

Chapter 7.2 Solving Two-Step Equations

� Your turn…

Chapter 7.2 Solving Two-Step Equations

�p336 (6–30 x 3)

�One Step Equations

�One-step equations with multiplication

�2-step equations

7-4: Circles and Circumference

� Objective: � To find the circumference of a circle

� Warm-Up: 1. 20 = 6x + 8 2. -10 – k = -36 3. 2y – 7 = 15 4. 15- 4g = - 33 5. 2.1 = 0.8 – z

6. -17 + �

� = 3

7. ���

� 36

8. - 49 = �

+ 11

Answers:

1. x = 2 2. k = 26 3. y = 11 4. g = 12 5. z = - 1.3 6. t = 100 7. k = - 126 8. z = - 360

7-4: Circles and Circumference

� Notes:

7.4 Circles and Circumferences

� NOTES: Your Turn…Write the radius and then find the Circumference

Circumferences:

1. 9.42 cm

2. 25.12 mm

3. 3.14 cm

4. 12.874 dm

5. 160.328 m

6. 24.806 cm

7-4 Circles and Circumference

� Notes:

� Fun With Pie

� Pi Poem (First 5 digits)

� Pi Chain (First 5 digits)

� Write a story about Sir

Cumference and the Round Table

� Cookie and Plate Challenge

� String and a Cup

� Shuffle Pi

7-4 Circles and Circumference

� Notes:

π Sing the song “We Wish You a Happy Pi Day” by

Dianna sung to the tune of We Wish You a Merry

Christmas

We wish you a happy Pi Day

We wish you a happy Pi Day

We wish you a happy Pi Day

To you and to all

7-4 Circles and Circumference

Oh, number Pi

Oh, number Pi

Your digits are unending,

Oh, number Pi

Oh, number Pi

No pattern are you sending.

You're three point one four

one five nine,

And even more if we had time,

Oh, number Pi

Oh, number Pi

For circle lengths unbending.

� Notes:

Sing O Number Pi: (to the tune of "Oh Christmas Tree")

7-4 Circles and Circumferences

�P343 (6-28 EVEN) or Three Activities

�Radius diameter and circumference

7-5 Solving Equations with Variables on Each Side

� Objective: To solve equations with variables on each side

� Warm-Up: Please solve each equation

1) -5a -18= 7

2) 3+ 2b= - 7

3) 5 = 7(y – 3) – 2

4) m + 5 = 2

3

5) If he radius is 5cm, then what is the circumference?

Answers: 1) a = -5 2) b = -5 3) y = 4 4) m = 1 5) 31.4 cm

7-5 Solving Equations with Variables on Each Side

� NOTES: What is a “Like Term”?

What differences do you see in the two lists?

7-5 Solving Equations with Variables on Each Side

� NOTES: Collect and ADD the “Like Terms”:

7-5 Solving Equations with Variables on Each Side

� NOTES:

TIME FOR A CHALLENGE!

1) −20 = −4a − 6a

2) 10 = 1 − 2w + 5w

3) 8t − 2 = −9 + 7t

4) 4f + 3f = 7f

5) r − 8 = −(r + 4)

6) 3(x +1) - 5 = 3x - 2

7) 12m = −4(−6m − 3)

Answers 1)a= 2 2)w = 3 3)t = -7 4)All 5)r = 4 6)Null 7)m = - ½

HINT : “Null” means NO SOLUTION and it is NEVER true!

“All” means ALL NUMBERS are possible to make it true!

7-5 Solving Equations with Variables on Each Side

� NOTES:

7-5 Solving Equations with Variables on Each Side

� NOTES:

7-5 Solving Equations with Variables on Each Side

�p348-349 (4-28 Even)

�Equations with variables on both sides

�One step inequalities

7-6 Solving Multi-Step Inequalities

� Objective: To solve inequalities with more than one operation

� Warm-Up: Please solve each equation

1. 5a – 18 = 3a

2. -3b + 13 = -b – 3

3. 4(2x – 1) – 3 = 5(x – 5)

4. 7(y – 3) – 2 = 3(2y – 5) + 4

5. 4/7m + 5 =

2/7m – 3

Answers:

1) a = 9 2) b = 8 3) x = -6 4) y = 12 5) m = -28

7-6 Solving Multi-Step Inequalities

� NOTES:

7-6 Solving Multi-Step Inequalities

� NOTES:

7-6 Solving Multi-Step Inequalities

� NOTES:

Solve b – 8 ≥ 3b – 8 and check the solution. Graph the solution on a number line.

b – 8 ≥ 3b – 8 + 8 + 8

b ≥ 3b – 3b – 3b

–2b ≤≤≤≤ 0 -2 -2

b ≤ ≤ ≤ ≤ 0

Rule: If each side of an inequality is multiplied or divided by a negative number, the order symbol of the inequality must be reversed.

1. Add 8 to each side. 2. Subtract 3b from each side. 3. Divide each side by –2

4. And change ≥≥≥≥ to ≤≤≤≤.

Solve 5m - 8 > 12

+ 8 + 8

5m > 20

5 5

m > 4

5(4) – 8 = 12

1. Draw “the river”

2. Add 8 to both sides

3. Simplify

4. Divide both sides by 5

5. Simplify

6. Check your answer

7. Graph the solution

o 4 53

Solve 12 - 3a > 18 - 12 - 12

-3a > 6

-3 -3

a < -2

12 - 3(-2) = 18

1. Draw “the river”

2. Subtract 12 from both sides

3. Simplify

4. Divide both sides by -3

5. Simplify (Switch the inequality!)

6. Check your answer

7. Graph the solution

o -2 -1-3

Which graph shows the solution to: 2x - 10 ≥ 4?

1. .

2.

3.

4.

Answer NowAnswer Now

Solve 5m - 4 < 2m + 11

- 2m -2m

3m - 4 < 11

+ 4 + 4

3m < 15

3 3

m < 5

5(5) – 4 = 2(5) + 11

1. Draw “the river”

2. Subtract 2m from both sides

3. Simplify

4. Add 4 to both sides

5. Simplify

6. Divide both sides by 3

7. Simplify

8. Check your answer

9. Graph the solution

o 5 64

Solve 2r - 18 ≤ 5r + 3 -2r -2r

-18 ≤ 3r + 3

- 3 - 3

-21 ≤ 3r

3 3

-7 ≤ r or r ≥ -7

2(-7) – 18 = 5(-7) +3

1. Draw “the river”

2. Subtract 2r from both sides

3. Simplify

4. Subtract 3 from both sides

5. Simplify

6. Divide both sides by 3

7. Simplify

8. Check your answer

9. Graph the solution

● -7 -6-8

6) Solve -2x + 6 ≥ 3x - 4

1. x ≥ -2

2. x ≤ -2

3. x ≥ 2

4. x ≤ 2

Answer NowAnswer Now

Solve 26p - 20 > 14p + 64 -14p -14p

12p – 20 > 64

+ 20 + 20

12p > 84

12 12

p > 7

26(7) – 20 = 14(7) + 64

1. Draw “the river”

2. Subtract 14p from both sides

3. Simplify

4. Add 20 to both sides

5. Simplify

6. Divide both sides by 12

7. Simplify

8. Check your answer

9. Graph the solution

o 7 86

What are the values of x if 3(x + 4) - 5(x - 1) < 5?

1. x < -6

2. x > -6

3. x < 6

4. x > 6

Answer NowAnswer Now

7-6 Solving Multi-Step Inequalities

�p353 (6-30 EVEN)

�Inequalities on a number line

�Multi-step linear inequalities

7.8 - The Metric System

� Objective: To convert measurements within the metric system

� Warm-Up: Solve and Graph

1. 21 - 4t < 25

2. 18 + 6m > -24

3. - 5.72 < a

-20

BONUS: How can I move the decimal with multiplication?

Answers:

1) t > -1 2) m > -7 3) a < 114.4

BONUS: Multi/Divide by 10!