2-2 Solving Two-Step Equations

Warm UpSolve each equation. 1. 3 + x = 11 2. x – 7 = 19

3. 6x = 15 4.

Find a common denominator.

5.

6.

8 26

12

Possible answer: 6

Possible answer: 20

2-2 Solving Two-Step Equations

Preparation for 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

2-2 Solving Two-Step Equations

equivalent equations

Vocabulary

2-2 Solving Two-Step Equations

Additional Example 1A: Solving Two-Step Equations

Solve 18 = 4a + 10.

18 = 4a + 10 First a is multiplied by 4. Then 10 is added.

–10 –10

8 = 4a

2 = a

Subtract 10 from both sides.

8 = 4a is equivalent to 18 = 4a + 10.

Since a is multiplied by 4, divide both sides by 4 to undo the multiplication.

The solution set is {2}.

2-2 Solving Two-Step Equations

Solve the equation. Check your answer.

7.2 = 1.2y

1.5 = 1.2y – 5.7

Check It Out! Example 1b

Add 5.7 to both sides.

7.2 = 1.2y is equivalent to 1.5 = 1.2y – 5.7.

Since y is multiplied by 1.2, divide both sides by 1.2 to undo the multiplication.

The solution set is {6}.

First y is multiplied by 1.2. Then 5.7 is subtracted.

+ 5.7 +5.7

6 = y

1.5 = 1.2y – 5.7

2-2 Solving Two-Step Equations

Solve the equation. Check your answer.

Check It Out! Example 1c

n = 0

Subtract 2 from each side.

Since n is divided by 7, multiply both sides by 7 to undo the division.

The solution set is {0}.

First n is divided by 7. Then 2 is added.

–2 –2

= 0 = 0 is equivalent to + 2 = 2.

2-2 Solving Two-Step Equations

Additional Example 2A: Solving Two-Step Equations That Contain Fractions

Solve the equation.

Method 1 Use fraction operations.

Since is subtracted from , add to

both sides to undo the subtraction.

2-2 Solving Two-Step Equations

Additional Example 2A Continued

y = 16

Since y is divided by 8 multiply both sides by 8.

Simplify.

The solution set is {16}.

2-2 Solving Two-Step Equations

Check It Out! Example 2c

Solve the equation. Check your answer.

Method 1 Use fraction operations.

Since is subtracted from , add

to both sides to undo the subtraction.

2-2 Solving Two-Step Equations

Check It Out! Example 2c Continued

Simplify.

The solution set is {15}.n = 15

Since n is multiplied by multiply both

sides by the reciprocal, .

2-2 Solving Two-Step Equations

Check It Out! Example 2c Continued

Check

To check your solution, substitute 15 for n in the original equation.

2-2 Solving Two-Step Equations

Check It Out! Example 3b

Lynda has 12 CDs in her collection. She adds the same number of new CDs to her collection each month. After 7 months Lynda has 26 CDs. How many records does Lynda add each month?

The answer will be the number of records that Lynda adds each month.

• Lynda started with 12 records.

• Lynda adds records each month.

• At the end of 7 months she had 26 records.

Let r represent the number of records added monthly.

2-2 Solving Two-Step Equations

Months is total records

Solve33

7r + 12 = 26–12 –12

7r = 14

r = 2 records a month

Since 12 is added to 7r, subtract 12 from both sides to undo the addition.

Since r is multiplied by 7, divide both sides by 7 to undo the multiplication.

initial records

plus

7r = 2612+

Check It Out! Example 3b Continued

2-2 Solving Two-Step Equations

Look Back44

Check that the answer is reasonable. The number of records added per month is 2, so if Lynda started with 12 records and added the 2 per month for 7 months, the total number is equal to 26.

Check It Out! Example 3b Continued

2-2 Solving Two-Step EquationsLesson Quiz

Solve each equation.

1. 4y + 8 = 2 2. 3 + 2x = 11

3. 4.

4

–8

5. Nancy bought 5 rolls of color film and 6 rolls of black-and-white film. The 5 rolls of color film cost $15, and Nancy’s total was $39. Write and solve an equation to find the cost of one roll of black-and-white film.

6b + 15 = 39; $4