11-3 Solving Multi-Step Equations California Standards Preview of Grade 7 Simplify

numerical

AF1.3 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

Holt CA Course 1

11-3 Solving Multi-Step Equations Teacher Example 1: Combining Like Terms to Solve Equations Solve 12 – 7b + 10b = 18.

12 – 7b + 10b = 18 12 + 3b = 18

Combine like terms.

Subtract 12 from both sides.

– 12 – 12 3b = 6 3b = 6 3 3 b = 2

Divide both sides by 3.

Holt CA Course 1

11-3 Solving Multi-Step Equations Student Practice 1: Solve 14 – 8b + 12b = 62.

14 – 8b + 12b = 62 14 + 4b = 62

Combine like terms.

Subtract 14 from both sides.

– 14 – 14 4b = 48 4b = 48 4 4 b = 12

Divide both sides by 4.

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 Teacher Example 2: Using the Distributive Property to Solve Equations Solve 5(y – 2) + 6 = 21.

5(y – 2) + 6 = 21 5 (y) – 5 (2) + 6 = 21 5y – 10 + 6 = 21 5y – 4 = 21 + 4 + 4 5y = 25 5 5 y = 5

Distribute 5 on the left side.

Simplify.

Combine like terms.

Add 4 to both sides. Divide both sides by 5.

Holt CA Course 1

11-3 Solving Multi-Step Equations

Remember!

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

Holt CA Course 1

11-3 Solving Multi-Step Equations Student Practice 2: Solve 3(x – 3) + 4 = 28.

3(x – 3) + 4 = 28 3 (x) – 3 (3) + 4 = 28 3x – 9 + 4 = 28 3x – 5 = 28 + 5 + 5 3x = 33 3 3 x = 11

Distribute 3 on the left side.

Simplify.

Combine like terms.

Add 5 to both sides. Divide both sides by 3.

Holt CA Course 1

11-3 Solving Multi-Step Equations Teacher Example 3: Problem Solving Application 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?

Holt CA Course 1

11-3 Solving Multi-Step Equations Teacher Example 3 Continued 1 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.

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11-3 Solving Multi-Step Equations Teacher Example 3 Continued 2 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.

Holt CA Course 1

11-3 Solving Multi-Step Equations Teacher Example 3 Continued 3 Solve

3c + c – 8 = 24 4c – 8 = 24 + 8 + 8 4c = 32

Combine like terms.

Add 8 to both sides.

4c = 32 4 4 c = 8

Divide both sides by 4.

Hillary owns 8 cards.

Holt CA Course 1

11-3 Solving Multi-Step Equations Teacher Example 3 Continued 4 Look Back

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.

Holt CA Course 1

11-3 Solving Multi-Step Equations Student Practice 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 Equations Student Practice 3: 1 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 Student Practice 3: 2 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.

Holt CA Course 1

11-3 Solving Multi-Step Equations Student Practice 3: 3 Solve

2h + h – 4 = 29 3h – 4 = 29 + 4 + 4 3h = 33

Combine like terms.

Add 4 to both sides.

3h = 33 3 3 h = 11 Hiro is 11 years old.

Divide both sides by 3.

Holt CA Course 1

11-3 Solving Multi-Step Equations Student Practice 3: 4 Look Back

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.

Holt CA Course 1

11-3 Solving Multi-Step Equations Solve.

11.3 Warm-Up

1. –x – 11 + 17x = 53 2. 4(k – 3) + 1 = 33 3. 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?

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11-3 Solving Multi-Step Equations 11.3 Day 2 Warm-Up Solve.

1. c + 21 + 5c = 63 2. 59 = w – 16 + 4w 5. Ann earns 1.5 times her normal hourly pay for each hour that she works over 40 hours in a week. Last week she worked 51 hours and earned $378.55.

What is her normal hourly pay?

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