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PPT – AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. PowerPoint presentation | free to download - id: 5a4f56-MDgwZ

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AF4.1 Solve two-step linear equations

and inequalities in one variable over the

rational numbers, interpret the solution or

solutions in the context from which they arose,

and verify the reasonableness of the results.

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.

Additional Example 1 Problem Solving Application

The mechanics bill to repair Mr. Wongs 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?

Additional Example 1 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

Additional Example 1 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.

Additional Example 1 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. Wongs

car.

Additional Example 1 Continued

You can use a table to decide whether your answer

is reasonable.

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.

Check It Out! Example 1

The mechanics 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?

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

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.

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.

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.

Additional Example 2A Solving Two-Step Equations

Solve 7 22.

Method 1 Use fraction operations.

Since n is divided by 3, multiply both sides by 3.

n 45

Additional Example 2B Solving Two-Step Equations

Solve 9.

Method 2 Multiply both sides of the equation by

the denominator.

Multiply both sides by the denominator.

y 4 27

4 4 Since 4 is subtracted from y, add

4 to both sides to undo the subtraction.

y 31

Check It Out! Example 2A

Solve 8 18.

Method 1 Use fraction operations.

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

n 40

Check It Out! Example 2B

Solve 7.

Method 2 Multiply both sides of the equation by

the denominator.

Multiply both sides by the denominator.

y 7 14

7 7 Since 7 is subtracted from y,

add 7 to both sides to undo the

subtraction.

y 21

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