Algebra I

Chapter 2 NotesLinear Equations

Section 2-1 Writing Equations

Ex1) Translate each sentence into an equation. Pay attention to the words is, is as much as, is the same as, is identical toa) Seven times a numbers squared is five times

the difference of k and m

b) Fifteen times a number subtracted from 80 is 25

Section 2-1

Ex2) Translate the sentence into a formula: the area of a triangle equals the product of ½ the length of the base and the height

Ex3) Translate each equation into a sentencea) 6z – 15 = 45 b)

Section 2-2: Solving One-Step Equations

Solution –

Equivalent Equations – Property Name Symbols Example

Addition Prop. Of Equality

Subtraction Prop. Of Equality

Multiplication Prop. Of Equality

Division Prop. Of Equality

Section 2-2: Solving One-Step Equations

Solution – the value(s) that make an equation true

Equivalent Equations – equations that have the same solution

Property Name Symbols Example

Addition Prop. Of Equality

Subtraction Prop. Of Equality

Multiplication Prop. Of Equality

Division Prop. Of Equality

Section 2-2

Ex1) Solve the one-step equations and check your answer!a) x – 22 = 54 b) y + 63 = 79

c) 3m = -12 d)

e)f) 5 = -6 + n

Section 2-2

Ex2) Of a group of female students surveyed, 225 or about said they talk on the phone while they watch t.v. How many girls were surveyed?

Section 2-2

Ex3) Solvea) g + 5 = 33 b) 104 = y –

67

c)d)

Section 2-3 Solving Multi-Step Equations

Ex1) Solvea) 11x – 4 = 29 b)

c) 2a – 6 = 4 d)

Section 2-3

Ex2) Sarah is buying a pair of water skis that are on sale for 2/3 of the original price. After he uses a $25 gift certificate, the total cost before taxes is $115. What was the original price of the skis? Write an equation and solve.

Section 2-3

Consecutive Integers – integers in counting order

Type Words Symbols Example

Consecutive Integers Integers in counting order

Consecutive Even Integers

Even integers in counting order

Consecutive Odd Integers

Odd integers in counting order

Section 2-3

Ex3) Write an equation for the following problem, then solve the equation. Find 3 consecutive odd integers with a sum of -51

Section 2-4: Solving Equations with Variables on Both Sides

Steps for Solving Equations with Multiple Steps1.

2.

3.

4.

5.

Section 2-4: Solving Equations with Variables on Both Sides

Steps for Solving Equations with Multiple Steps1. Distribute (get rid of parenthesis)

2. Combine Like terms on the same side of =

3. Get variables together on one side of =

4. Add or subtract the number NOT attached to the variable

5. Multiply or divide the number that IS attached to the variable

Section 2-4

Ex1) Solvea) 2 + 5k = 3k – 6 b) 3w + 2 = 7w

c) 5a + 2 = 6 – 7a d)

Section 2-4: Equations with Grouping Symbols

Ex2) a) b) 8s – 10 = 3(6 – 2s)

c) 7(n – 1) = -2(3 + n)

Section 2-4: Special Solutions

Ex2) Solvea) 5x + 5 = 3(5x – 4) – 10x b) 3(2b – 1) – 7 = 6b – 10

Section 2-4

Find the value of x so that the figures have the same area

10cmx cm

6 cm3cm x cm

Find the value of x so that the figures have the same perimeter

x6

x

2x + 2

Section 2-5: Solving Equations Involving Absolute Value

Absolute Value – The distance a point is from zero on a number line

Ex1) Evaluatea) if m = 4 b)

if x = 2

Section 2-5

Solve the absolute value equationEx2)

Steps1. Split the equation into

2 equations, one that = the positive number and one that = the negative number

2. Solve each equation (you will have 2 answers!)

Section 2-5

Ex3) Solvea) b)

c)

Section 2-6: Ratios and Proportions

Ratio –

Proportion –

Means-Extremes Property of ProportionWords

Symbols

Examples

Section 2-6: Ratios and Proportions

Ratio – A comparison between two numbers using division (fraction)

Proportion – two ratios that are equal

Means-Extremes Property of ProportionWords In a proportion, the product of the extremes is equal to the product of the means

Symbols If , and b and d do not equal zero, then ad = bc

Examples Since , 2(2) = 4(1) or 4 = 4

Section 2-6

Ex1) Determine if the ratios are equivalent. Answer yes or no.a) b)

c)

Section 2-6

Ex2) Use cross-multiplication to solve the proportionsa) b)

c)

Section 2-6

Ex3) The Ramsey Cascades Trail is about inches long on a map with a scale of 3 in = 10 miles. What is the actual length of the trail. Let l represent the length.

Section 2-6 Day 2 The Percent Proportion

• Use the percent proportion to solve the following.

a) 15 is what percent of 105?

b) What is 35% of 125?

c) 23 is 55% of what number?

100

%

of

is

Chapter 2 Word ProblemsDraw a picture to represent the situation, then setup an

equation and solve. 1) A page of the school yearbook is 8.5 by 11 inches. The left and

right margins are 1.5 inches and 2.5 inches, respectively. The space between pictures is 0.5 inches. How wide can each picture be to fit 3 across the width of the page?

Chapter 2 Word Problems (cont.)Draw a picture to represent the situation, then setup an

equation and solve. 2) While on business, Carrie drive 80 miles per hour in a car and

traveled 300 miles per hour in a plane. She drove twice as many hours as she flew and the total mileage for the trip was 1000 miles. How many hours did she drive?

Chapter 2 Word Problems (cont.)Draw a picture to represent the situation, then setup an

equation and solve. 3) A gym charges non-members $15 per day to use the pool.

Members pay a yearly fee of $200 and $4 per day to use the pool. Find how many days you must use the pool to justify becoming a member.