HW # 25- p. 100 # 15-29 all BRING AN EGG CARTON Warm up

Week 7, Day One

Solve.

a) Y + 16.7 = -49d) - h = 2

7.8b) 4.7m = -32.9

c) k-3.2 = -6.8

Warm Up ResponseSolve.

a) Y + 16.7 = -49 -65.7 d) - h = 2 -15.6

7.8b) 4.7m = -32.9 -7

c) k-3.2 = -6.8 -3.6

Goals for Today

• 2-8 Two-Step Equations with Rational Numbers

Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solving, ask yourself,

“What is being done to the variable, and in what order?”

One method to solve the equation is to work backward to undo the operations.

The mechanic’s bill to repair Mr. Wong’s car was $653.05. The mechanic charges $45.50 an hour for labor, and the parts that were used cost $443.75. How many hours did the mechanic work on the car?

Problem Solving Application

Continued

1 Understand the Problem

The answer is the number of hours the mechanic worked on the car.

List the important information:

Let h represent the hours the mechanic worked.

• The parts cost $443.75.• The labor cost $45.50 per hour.• The total bill was $653.05.

Total bill = Parts + Labor

653.05 = 443.75 + 45.50h

Think: First the variable is multiplied by 45.50, and then 443.75 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443.75 from both sides of the equation, and then divide both sides of the new equation by 45.50.

2 Make a Plan

Continued

653.05 = 443.75 + 45.50h

Solve3

–443.75 –443.75

209.30 = 45.50h

4.6 = h

The mechanic worked for 4.6 hours on Mr. Wong’s car.

Continued

Since h is multiplied by 45.50, divide both sides by 45.50.209.30 45.50h

45.50 45.50=

Since 443.75 is added to both sides, subtract 443.75 from both sides.

You can use a table to decide whether your answer is reasonable.Look Back4

Continued

Hours Labor Parts Total Cost

1 $45.50 $443.75 $489.25

2 $91.00 $443.75 $534.75

3 $136.50 $443.75 $580.25

4 $182.00 $443.75 $625.75

5 $227.50 $443.75 $671.25

4.6 hours is a reasonable answer.

Example 2

n + 7 = 22 3

n + 7 = 22 3 -7 -7

n = 15 3

3 * n = 15 * 3 3

n = 45

Example 3

Solve = 9.y – 4 3

= 9y – 43

y – 4 = 27

+ 4 + 4 Since 4 is subtracted from y, add 4 to

both sides to undo the subtraction.y = 31

Multiply both sides by the denominator.

Method 2: Multiply both sides of the equation by the denominator.

= 9y – 43(3) (3)

Example 4

Solve + 8 = 18.N

4

+ 8 – 8 = 18 – 8n4

Since n is divided by 4, multiply both sides by 4.4 = 4 10N

4n = 40

Method 1: Use fraction operations.

+ 8 = 18N

4 Since 8 is added to ,

subtract 8 from both sides to undo the addition.

n4

= 10N

4

Solve.

1. – x – 3 = 10

2. 7y + 25.68 = –26.12

3. –8.3 = –3.5x + 13.4

4. = 3.1

5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1032.96, how many months will the contract last?

Lesson Quiz

y = –7.4

x = –117

x = 6.2

y = 29.1

24 months

19

y + 5 11

The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?

EXTRA EXAMPLES: Example 1

Check It Out! Example 1 Continued

1 Understand the Problem

The answer is the number of hours the mechanic worked on your car.

List the important information:

Let h represent the hours the mechanic worked.

• The parts cost $275.• The labor cost $35 per hour.• The total bill was $850.

Total bill = Parts + Labor

850 = 275 + 35h

Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35.

2 Make a Plan

Check It Out! Example 1 Continued

850 = 275 + 35h

Solve3

–275 –275

575 = 35h

16.4 h

The mechanic worked for about 16.4 hours on your car.

Check It Out! Example 1 Continued

575 35h35 35

=

Since h is multiplied by 35, divide both sides by 35.

Since 275 is added to both sides, subtract 275 from both sides.

Look Back4

Check It Out! Example 1 Continued

You can use a table to decide whether your answer is reasonable.

Hours Labor Parts Total Cost

13 $455 $275 $730

14 $490 $275 $765

15 $525 $275 $800

16 $560 $275 $835

17 $595 $275 $870

16.4 hours is a reasonable answer.