Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

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Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Warm UpSolve.

1. 6n + 8 – 4n = 20

2. –4w + 16 – 4w = –32

3. 25t – 17 – 13t = 67

4. 12 = 2(x + 7) + 4

n = 6

w = 6

t = 7

x = –3

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Objective:Objective: You will learn how to You will learn how to solve equations that have variables solve equations that have variables on both sides.on both sides.

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Preview of Algebra 1 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

California Standards

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Group the terms with variables on one side of the equal sign, and simplify.

Additional Example 1: Using Inverse Operations to Group Terms with Variables

A. 60 – 4y = 8y B. –5b + 72 = –2b

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Group the terms with variables on one side of the equal sign, and simplify.

A. 40 – 2y = 6y B. –8b + 24 = –5b

Check It Out! Example 1

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Solve.

Additional Example 2A: Solving Equations with Variables on Both Sides

7c = 2c + 55

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Additional Example 2B: Solving Equations with Variables on Both Sides

Solve.

49 – 3m = 4m + 14

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Additional Example 2C: Solving Equations with Variables on Both Sides

25

x = 15

x – 12

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Solve.8f = 3f + 65

Check It Out! Example 2A

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Solve.

54 – 3q = 6q + 9

Check It Out! Example 2B

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

23

w = 13

w – 9

Check It Out! Example 2C

Solve.

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Christine can buy a new snowboard for $136.50. She will still need to rent boots for $8.50 a day. She can rent a snowboard and boots for $18.25 a day. How many days would Christine need to rent both the snowboard and the boots to pay as much as she would if she buys the snowboard and rents only the boots for the season?

Additional Example 3: Consumer Math Application

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Additional Example 3 Continued

18.25d = 136.5 + 8.5d

9.75d = 136.5

9.75d = 136.5

9.75 9.75d = 14

Let d represent the number of days.

Subtract 8.5dfrom both sides.

Simplify.

Divide both sides by 9.75.

Christine would need to rent both the snowboard and the boots for 14 days to pay as much as she would have if she had bought the snowboard and rented only the boots.

– 8.5d – 8.5d

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Check It Out! Example 3

A local telephone company charges $40 per month for services plus a fee of $0.10 a minute for long distance calls. Another company charges $75.00 a month for unlimited service. How many minutes does it take for a person who subscribes to the first plan to pay as much as a person who subscribes to the unlimited plan?

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Check It Out! Example 3 Continued

Let m represent the number of minutes.

75 = 40 + 0.10m

350 = m

Subtract 40from both sides.

Simplify.

If you are going to use more than 350 minutes, it will be cheaper to subscribe to the unlimited plan.

Divide both sides by 0.10.

35 = 0.10m

35 0.10m 0.10 0.10

=

–40 –40

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

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Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Lesson Quiz: Part I

Group the terms with variables on one side of the equal sign, and simplify.

1. 14n = 11n + 81

2. –14k + 12 = –18k

Solve.

3. 58 + 3y = –4y – 19

4. –6x = x – 112

4k = –12

3n = 81

y = –11

x = 16

Holt CA Course 1

11-4 Solving Equations with Variables on Both Sides

Lesson Quiz Part II

5. Mary can purchase ice skates for $57 and then

pay a $6 entry fee at the ice skating rink. She

can also rent skates there for $3 and pay the

entry fee. How many times must Mary skate to

pay the same amount whether she purchases

or rents the skates?

19 times