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

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

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HW # 25- p. 100 # 15-29 all

BRING AN EGG CARTON

Warm up

Solve.

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

7.8

b) 4.7m = -32.9

c) k-3.2 = -6.8

Solve.

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

7.8

b) 4.7m = -32.9 -7

c) k-3.2 = -6.8 -3.6

- 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.

Problem Solving Application therefore,

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?

1 therefore,

Understand the Problem

Continued

List the important information:

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

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

Let h represent the hours the mechanic worked.

Total bill = Parts + Labor

653.05 = 443.75 + 45.50h

Make a Plan therefore,

2

Continued

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.

3 therefore,

Solve

209.30 45.50h

=

45.5045.50

Continued

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

653.05 = 443.75 + 45.50h

–443.75–443.75

209.30 = 45.50h

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

4.6 = h

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

4 therefore,

Look Back

Continued

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

4.6 hours is a reasonable answer.

y therefore, – 4

y – 4

y – 4

3

3

3

= 9

= 9

(3) (3)

Example 3

Solve = 9.

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

Multiply both sides by the denominator.

y – 4 = 27

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

both sides to undo the subtraction.

y = 31

N therefore,

4

n4

N

4

N

4

n4

N

4

+ 8 = 18

= 10

Since 8 is added to ,

subtract 8 from both sides to undo the addition.

+ 8 – 8= 18 – 8

4 = 4 10

Example 4

Solve + 8 = 18.

Method 1: Use fraction operations.

Since n is divided by 4, multiply both sides by 4.

n = 40

1 therefore,

9

y + 5 11

Lesson Quiz

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?

x = –117

y = –7.4

x = 6.2

y = 29.1

24 months

EXTRA EXAMPLES: therefore, Example 1

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?

1 therefore,

Understand the Problem

Check It Out! Example 1 Continued

List the important information:

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

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

Let h represent the hours the mechanic worked.

Total bill = Parts + Labor

850 = 275 + 35h

Make a Plan therefore,

2

Check It Out! Example 1 Continued

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.

3 therefore,

Solve

575 35h

=

3535

Check It Out! Example 1 Continued

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

850 = 275 + 35h

–275–275

575 = 35h

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

16.4 h

The mechanic worked for about 16.4 hours on your car.

4 therefore,

Look Back

Check It Out! Example 1 Continued

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

16.4 hours is a reasonable answer.

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