Student Learning Goal Chart

Chapter 10

Pre-Algebra Learning Goal

Students will understand solving linear equations and inequalities.

Students will understand solving linear equations and inequalities by being able to do the following:

• Learn to solve two-step equations (10.1)

Pre-Algebra

10-1 Solving Two-Step Equations

Today’s Learning Goal Assignment

Learn to solve two-step equations.

Pre-Algebra

10-1 Solving Two-Step Equations

Pre-Algebra HW

Page 500#15-32

Pre-Algebra

10-1 Solving Two-Step Equations10-1 Solving Two-Step Equations

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

10-1 Solving Two-Step Equations

Warm UpSolve.

1. x + 12 = 35

2. 8x = 120

3. = 7

4. –34 = y + 56

x = 23

x = 15

y = 63

Pre-Algebra

10-1 Solving Two-Step Equations

y = –90

y9

Pre-Algebra

10-1 Solving Two-Step Equations

Problem of the Day

x is an odd integer. If you triple x and then subtract 7, you get a prime number. What is x? (Hint: Think about what the prime number must be in order for x to be an odd.)

x = 3

Pre-Algebra

10-1 Solving Two-Step Equations

Today’s Learning Goal Assignment

Learn to solve two-step equations.

Pre-Algebra

10-1 Solving Two-Step Equations

Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order?” Then work backward to undo the operations.

Pre-Algebra

10-1 Solving Two-Step Equations

The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?

Additional Example 1: Problem Solving Application

Pre-Algebra

10-1 Solving Two-Step Equations

Additional Example 1 Continued

11 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.• The labor cost $45 per hour.• The total bill was $650.

Total bill = Parts + Labor

650 = 443 + 45h

Pre-Algebra

10-1 Solving Two-Step Equations

Think: First the variable is multiplied by 45, and then 443 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443 from both sides of the equation, and then divide both sides of the new equation by 45.

22 Make a Plan

Additional Example 1 Continued

Pre-Algebra

10-1 Solving Two-Step Equations

650 = 443 + 45h

Solve33

–443 –443 Subtract to undo the addition.

207 = 45h

4.6 = h

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

Additional Example 1 Continued

Divide to undo multiplication.207 45h45 45=

Pre-Algebra

10-1 Solving Two-Step Equations

If the mechanic worked 4.6 hours, the labor would be $45(4.6) = $207. The sum of the parts and the labor would be $443 + $207 = $650.

Look Back44

Additional Example 1 Continued

Pre-Algebra

10-1 Solving Two-Step Equations

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?

Try This: Example 1

Pre-Algebra

10-1 Solving Two-Step Equations

Try This: Example 1 Continued

11 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

Pre-Algebra

10-1 Solving Two-Step Equations

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.

22 Make a Plan

Try This: Example 1 Continued

Pre-Algebra

10-1 Solving Two-Step Equations

850 = 275 + 35h

Solve33

–275 –275 Subtract to undo the addition.

575 = 35h

16.4 h

The mechanic worked for about 16.4 hours on your car.

Try This: Example 1 Continued

Divide to undo multiplication.575 35h35 35=

Pre-Algebra

10-1 Solving Two-Step Equations

If the mechanic worked 16.4 hours, the labor would be $35(16.4) = $574. The sum of the parts and the labor would be $275 + $574 = $849.

Look Back44

Try This: Example 1 Continued

Pre-Algebra

10-1 Solving Two-Step Equations

Additional Example 2A: Solving Two-Step Equations

A. + 7 = 22

Solve.

Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3.

– 7 – 7 Subtract to undo addition.

n3

+ 7 = 22n3

Multiply to undo division.3 = 3 15n3n = 45

n3

= 15

Pre-Algebra

10-1 Solving Two-Step Equations

Additional Example 2A Continued

Substitute 45 into the original equation.

Check + 7 = 22n3

? + 7 = 2245

315 + 7 = 22

?

Pre-Algebra

10-1 Solving Two-Step Equations

Additional Example 2B: Solving Two-Step Equations

B. 2.7 = –1.3m + 6.6

Think: First the variable is multiplied by –1.3, and then 6.6 is added. To isolate the variable, subtract 6.6, and then divide by –1.3.

2.7 = –1.3m + 6.6–6.6 –6.6 Subtract to undo addition.–3.9 = –1.3m

Divide to undo multiplication.

3 = m

–1.3 –1.3–3.9 = –1.3m

Pre-Algebra

10-1 Solving Two-Step Equations

Additional Example 2C: Solving Two-Step Equations

C. = 9y – 4 3

Think: First 4 is subtracted from the variable, and then the result is divided by 3. To isolate the variable, multiply by 3, and then add 4.

= 9y – 43

y – 4 = 27 + 4 + 4 Add to undo subtraction.

y = 31

3 · 3 · Multiply to undo division.= 9y – 43

Pre-Algebra

10-1 Solving Two-Step Equations

Try This: Example 2A

A. + 5 = 29

Solve.

Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4.

– 5 – 5 Subtract to undo addition.

n4

+ 5 = 29n4

Multiply to undo division.4 = 4 24n4

n = 96

Pre-Algebra

10-1 Solving Two-Step Equations

Substitute 96 into the original equation.

Check + 5 = 29n4

? + 5 = 2996

424 + 5 = 29

?

Try This: Example 2A Continued

Pre-Algebra

10-1 Solving Two-Step Equations

Try This: Example 2B

B. 4.8 = –2.3m + 0.2

Think: First the variable is multiplied by –2.3, and then 0.2 is added. To isolate the variable, subtract 0.2, and then divide by –2.3.

4.8 = –2.3m + 0.2–0.2 –0.2 Subtract to undo addition.4.6 = –2.3m

Divide to undo multiplication.

–2 = m

–2.3 –2.3 4.6 = –2.3m

Pre-Algebra

10-1 Solving Two-Step Equations

Try This: Example 2C

C. = 8y – 2 4

Think: First 2 is subtracted from the variable, and then the result is divided by 4. To isolate the variable, multiply by 4, and then add 2.

= 8y – 24

y – 2 = 32 + 2 + 2 Add to undo subtraction.

y = 34

4 · 4 · Multiply to undo division.= 8y – 24

Pre-Algebra

10-1 Solving Two-Step Equations

Solve.

1. – 3 = 10

2. 7y + 25 = –24

3. –8.3 = –3.5x + 13.4

4. = 3

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 $1014, how many months will the contract last?

Lesson Quiz

y = –7

x = –117

x = 6.2

y = 28

24 months

x–9

y + 5 11