Holt CA Course 1

11-3 Solving Multi-Step Equations

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Holt CA Course 1

11-3 Solving Multi-Step Equations

Warm UpSolve.

1. –8p – 8 = 56

2. 13d – 5 = 60

3. 9x + 24 = 60

4.

p = –8

d = 5

x = 4k7 + 4 = 11

5. 19 + z4 = 24

k = 49

z = 20

Holt CA Course 1

11-3 Solving Multi-Step Equations

Preview of Grade 7 AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used.Also covered: Preview of Algebra 1 5.0

California Standards

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve 12 – 7b + 10b = 18.

Additional Example 1: Combining Like Terms to Solve Equations

12 – 7b + 10b = 18

12 + 3b = 18

– 12 – 12

3b = 6

3b = 63 3

b = 2

Combine like terms.

Subtract 12 from both sides.

Divide both sides by 3.

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve 14 – 8b + 12b = 62.

14 – 8b + 12b = 62

14 + 4b = 62

– 14 – 14

4b = 48

4b = 484 4

b = 12

Combine like terms.

Subtract 14 from both sides.

Divide both sides by 4.

Check It Out! Example 1

Holt CA Course 1

11-3 Solving Multi-Step Equations

You may need to use the Distributive Property to solve an equation that has parentheses. Multiply each term inside the parentheses by the factor that is outside the parentheses. Then combine like terms.

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve 5(y – 2) + 6 = 21.

Additional Example 2: Using the Distributive Property to Solve Equations

5(y – 2) + 6 = 21

5(y) – 5(2) + 6 = 21

+ 4 + 4

5y = 25

5 5

y = 5

Distribute 5 on the left side.

Simplify.

Add 4 to both sides.

5y – 10 + 6 = 21

Divide both sides by 5.

Combine like terms.5y – 4 = 21

Holt CA Course 1

11-3 Solving Multi-Step Equations

The Distributive Property states that a(b + c) = ab + ac. For instance, 2(3 + 5) = 2(3) + 2(5).

Remember!

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve 3(x – 3) + 4 = 28.

Check It Out! Example 2

3(x – 3) + 4 = 28

3(x) – 3(3) + 4 = 28

+ 5 + 5

3x = 333 3

x = 11

Distribute 3 on the left side.

Simplify.

Add 5 to both sides.

3x – 9 + 4 = 28

Divide both sides by 3.

Combine like terms.3x – 5 = 28

Holt CA Course 1

11-3 Solving Multi-Step Equations

Troy has three times as many trading cards as Hillary. Subtracting 8 from the combined number of trading cards Troy and Hillary have gives the number of cards Sean has. If Sean owns 24 trading cards, how many trading cards does Hillary own?

Additional Example 3: Problem Solving Application

Holt CA Course 1

11-3 Solving Multi-Step EquationsAdditional Example 3 Continued

11 Understand the Problem

Rewrite the question as a statement.

• Find the number of trading cards that Hillary owns.

List the important information:

• Troy owns 3 times as many trading cards as Hillary.

• Subtracting 8 from the combined number of trading cards Troy and Hillary own gives the number cards Sean owns.

• Sean owns 24 trading cards.

Holt CA Course 1

11-3 Solving Multi-Step Equations

22 Make a Plan

Let c represent the number of trading cards Hillary owns. Then 3c represents the number Troy owns.

Troy’s cards + Hillary’s cards – 8 = Sean’s cards

3c + c – 8 = 24

Solve the equation 3c + c – 8 = 24 for c.

Additional Example 3 Continued

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve33

3c + c – 8 = 24

4c – 8 = 24

+ 8 + 8

4c = 324 4

c = 8

Hillary owns 8 cards.

Combine like terms.

Add 8 to both sides.

Divide both sides by 4.

Additional Example 3 Continued

4c = 32

Holt CA Course 1

11-3 Solving Multi-Step Equations

Look Back44

Make sure that your answer makes sense in the original problem. Hillary owns 8 cards. Troy owns 3(8) = 24 cards. Sean owns 24 + 8 – 8 = 24.

Additional Example 3 Continued

Holt CA Course 1

11-3 Solving Multi-Step EquationsCheck It Out! Example 3

John is twice as old as Hiro. Subtracting 4 from the combined age of John and Hiro gives William’s age. If William is 29, how old is Hiro?

Holt CA Course 1

11-3 Solving Multi-Step EquationsCheck It Out! Example 3 Continued

11 Understand the Problem

Rewrite the question as a statement.

• Find Hiro’s age.

List the important information:

• John is 2 times as old as Hiro.

• Subtracting 4 from the combined age of John and Hiro gives William’s age.

• William is 29 years old.

Holt CA Course 1

11-3 Solving Multi-Step Equations

22 Make a Plan

Let h represent Hiro’s age. Then 2h represents John’s age.

John’s age + Hiro’s age – 4 = William’s age

2h + h – 4 = 29

Solve the equation 2h + h – 4 = 29.

Check It Out! Example 3 Continued

Holt CA Course 1

11-3 Solving Multi-Step Equations

Solve33

2h + h – 4 = 29

3h – 4 = 29

+ 4 + 4

3h = 333 3

h = 11

Hiro is 11 years old.

Combine like terms.

Add 4 to both sides.

Divide both sides by 3.

3h = 33

Check It Out! Example 3 Continued

Holt CA Course 1

11-3 Solving Multi-Step Equations

Look Back44

Make sure that your answer makes sense in the original problem. Hiro is 11 years old, then John is 2(11) = 22 years old. William is 22 + 11 – 4 = 29 years old.

Check It Out! Example 3 Continued

Holt CA Course 1

11-3 Solving Multi-Step EquationsLesson Quiz

Solve.

1. c + 21 + 5c = 63

2. –x – 11 + 17x = 53

3. 59 = w – 16 + 4w

4. 4(k – 3) + 1 = 33

x = 4

c = 7

15 = w

k = 11

5. Kelly swam 4 times as many laps as Kathy. Adding 5 to the number of laps Kelly swam gives you the number of laps Julie swam. If Julie swam 9 laps, how many laps did Kathy swim? 1 lap