1. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
SOLUTION
7p + 13 = 9p – 5
Write original equation.
13 = 2p – 5
Subtract 7p from each side.
18 = 2p
Add 5 to each side.
9 = p
Divide each side by 2.
ANSWER
The correct answer is D

2. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
CHECK
7p + 13 = 9p – 5
Write original equation.
7(9) (9) – 5 = ?
Substitute 9 for p.
– 5 = ?
Multiply.
76 = 76
Solution checks.

3. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
Solve 3(5x – 8) = –2(–x + 7) – 12x.
3(5x – 8) = –2(–x + 7) – 12x
Write original equation.
15x – 24 = 2x – 14 – 12x
Distributive property
15x – 24 = – 10x – 14
Combine like terms.
25x – 24 = –14
Add 10x to each side.
25x = 10
Add 24 to each side.
x = 2 5
Divide each side by 25 and simplify.
ANSWER
The solution 2 5

4. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
CHECK 2 5
3( – 8) –2(– ) – 12 = ? 2 5
Substitute for x.
3(–6) –14 – 4 5 = ? 24
Simplify.
– 18 = – 18
Solution checks.

5. EXAMPLE 5
Solve a work problem
Car Wash
It takes you 8 minutes to wash a car and it takes a friend 6 minutes to wash a car. How long does it take the two of you to wash 7 cars if you work together?
SOLUTION
STEP 1
Write a verbal model. Then write an equation.

6. Solve the equation for t. STEP 2 1 8 t + t = 7 6
EXAMPLE 5
Solve a work problem
Solve the equation for t.
STEP 2 1 8
t t = 7 6
Write equation.
24( t t) = 24 (7) 1 8 6
Multiply each side by the LCD, 24.
3t + 4t = 168
Distributive property
7t = 168
Combine like terms.
t = 24
Divide each side by 7.
ANSWER
It will take 24 minutes to wash 7 cars if you work together.

7. EXAMPLE 5
Solve a work problem
CHECK
You wash = 3 cars and your friend washes = 4 cars in 24 minutes. Together, you wash 7 cars. 1 6 8

8. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
5. –2x + 9 = 2x – 7
ANSWER
The correct answer is 4.
– x = –6x + 15
ANSWER
The correct answer is 1.
(x + 2) = 5(x + 4)
ANSWER
The solution is –7.

9. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
8. –4(2x + 5) = 2(–x – 9) – 4x
ANSWER
The solution x = – 1
x x = 39 1 4 2 5 9.
ANSWER
The correct answer is 60

10. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
x = x – 1 2 3 5 6
ANSWER
The correct answer is 4
What If? In Example 5, suppose it takes you 9 minutes to wash a car and it takes your friend 12 minutes to wash a car. How long does it take the two of you to wash 7 cars if you work together?
11.
ANSWER
It will take 36 minutes to wash 7 cars if you work together.