10-1

Pre-Algebra

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

Pre-Algebra

Homework & Learning GoalHomework & Learning Goal

Lesson PresentationLesson Presentation

AIMS PrepAIMS Prep

Pre-Algebra

10-1 Solving Two-Step Equations

Pre-Algebra HOMEWORK

Page 500

#8-30 EVENS

Pre-Algebra

10-1 Solving Two-Step Equations

Our Learning GoalStudents will be able to solve

multi-step equations with multiple variables, solve

inequalities and graph the solutions on a number line.

Pre-Algebra

10-1 Solving Two-Step Equations

Our Learning Goal Assignments• Learn to solve two-step equations.

• Learn to solve multistep equations.

• Learn to solve equations with variables on both sides of the equal sign.

• Learn to solve two-step inequalities and graph the solutions of an inequality on a number line.

• Learn to solve an equation for a variable.

• Learn to solve systems of equations.

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 & 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

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

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

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

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 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?

Don’t forget your proper heading! Trade & Grade!

10-1 Lesson Quiz

y = –7

x = –117

x = 6.2

y = 28

24 months

x–9

y + 5 11

Pre-Algebra

10-1 Solving Two-Step Equations

6th Grade AIMS PrepWhen you play a game with a friend, there are lots of tricks, or strategies, that you use to win the game.

Just like the game tricks, there are lots of test-taking tricks to help you “win” when taking the AIMS Math Test.

What are some test-taking tricks that you use?

AIMS Example 1What is the problem asking us to solve?

Test-Taking Strategy #1Understand the problem!! Read It Thoroughly!