EXAMPLE 3 Standardized Test Practice

SOLUTION

7p + 13 = 9p – 5

13 = 2p – 5

18 = 2p

9 = p

Write original equation.

Subtract 7p from each side.

Add 5 to each side.

Divide each side by 2.

ANSWER The correct answer is D

EXAMPLE 3 Standardized Test Practice

CHECK

7p + 13 = 9p – 5

7(9) + 13 9(9) – 5=?

63 + 13 81 – 5=?

76 = 76

Write original equation.

Substitute 9 for p.

Multiply.

Solution checks.

EXAMPLE 4 Solve an equation using the distributive property

Solve 3(5x – 8) = – 2(– x + 7) – 12x.

3(5x – 8) = – 2(– x + 7) – 12x

15x – 24 = 2x – 14 – 12x

15x – 24 = – 10x – 14

25x – 24 = –14

25x = 10

x = 25

Write original equation.

Distributive property

Combine like terms.

Add 10x to each side.

Add 24 to each side.

Divide each side by 25 and simplify.

ANSWER The solution 25

EXAMPLE 4 Solve an equation using the distributive property

CHECK

3 (5 – 8) – 2(– +7) – 12 25

25

25=?

3( – 6) –14 – 45=? 24

5

– 18 = – 18

25

Substitute for x.

Simplify.

Solution checks.

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.

EXAMPLE 5 Solve a work problem

Solve the equation for t.STEP 2

18

t + t = 716

24( t + t) = 24 (7)18

16

3t + 4t = 168

7t = 168

t = 24

Write equation.

Multiply each side by the LCD, 24.

Distributive property

Combine like terms.

Divide each side by 7.

ANSWER It will take 24 minutes to wash 7 cars if you work together.

EXAMPLE 5 Solve a work problem

CHECK

You wash 24 = 3 cars and your friend washes 24 = 4 cars in 24 minutes. Together,

you wash 7 cars.

16

18

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

5. –2x + 9 = 2x – 7

SOLUTION

–2x + 9 = 2x – 7

–4x + 9 = – 7

–4x = –16

x = 4

Write original equation.

Subtract 2x from each side.

subtract 9 from each side.

Divide each side by –4.

ANSWER The correct answer is 4.

GUIDED PRACTICE for Examples 3, 4, and 5

CHECK

–2(4) + 9 2(4) – 7?= Substitute 4 for x.

–8 + 9 = 8 – 7

1 = 1 Solution check

Simplify

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

6. 10 – x = – 6x + 15

SOLUTION

10 – x = – 6x + 15

10 + 5x = 15

5x = 5

x = 1

Write original equation.

Add 6x to each side.

subtract 10 from each side.

Divide each side by –5.

ANSWER The correct answer is 1.

GUIDED PRACTICE for Examples 3, 4, and 5

CHECK

10 –1 – 6(1) + 15?= Substitute 1 for x.

9 = 9 Solution check.

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

7. 3(x + 2) = 5(x + 4)

SOLUTION

3(x + 2) = 5(x + 4)

3x + 6 = 5x + 20

6 = 2x + 20

x = –7

Write original equation.

Distributive property.

Subtract 3x from each side.

Solve for x

ANSWER The solution is –7.

– 14 = 2x Subtract 20 from each side.

GUIDED PRACTICE for Examples 3, 4, and 5

CHECK

3((–7) + 2) 5 (–7 + 4)?= Substitute – 7 for x.

Solution check.

3(–5) 5 (–3)?=

– 15 = –15

Simplify

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

8. – 4(2x + 5) = 2(– x – 9) – 4x

SOLUTION

– 4(2x + 5) = 2(–x – 9) – 4x

–8x – 20 = –2x – 18 – 4x

–8x – 20 = –6x – 18

–20 = 2x – 18

Write original equation.

Distributive property.

Combine like term.

Divide each side by 2.x = –1

Add 8x to each side.

Add 18 to each side.–2 = 2x

GUIDED PRACTICE for Examples 3, 4, and 5

ANSWER The solution x = – 1

CHECK

–4 (2(–1) + 5 ) 2(–(–1) – 9) – 4(–1)

=?

– 4( – 2 + 5) 2 (– 8) + 4 =?

Substitute –1 for x.

Simplify.

Solution checks.

– 4( 3) (–16) + 4 =?

– 12 = –12

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

x + x = 3914

25

9.

SOLUTION

x = 60

Write original equation.

Combine like term.

Multiply each side by 20.

Divide each side to 13.

ANSWER The correct answer is 60

x + x = 3914

25

13x20

= 39

13x = 39 20

CHECK

Write original equation.

Substitute 60 for x.

Simplify

Solution checks.

GUIDED PRACTICE for Examples 3, 4, and 5

14 (60) + (60) 392

5?=

?=120

5+ 604

39

39 = 39

x + x = 3914

25

GUIDED PRACTICE for Examples 3, 4, and 5

Solve the equation. Check your solution.

10. x+ = x – 12

23

56

ANSWER The correct answer is 4

GUIDED PRACTICE for Examples 3, 4, and 5

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.

STEP 1 Write a verbal model. Then write an equation.

SOLUTION

t min1 car9 min

1 car12 min

t min = 7+

Solve the equation for t.STEP 219

t + t = 7112

36( t + t) = 36 (7)19

112

4t + 3t = 252

7t = 252

t = 36

Write equation.

Multiply each side by the LCD, 24.

Distributive property

Combine like terms.

Divide each side by 7.

ANSWER It will take 36 minutes to wash 7 cars if you work together.

GUIDED PRACTICE for Examples 3, 4, and 5

EXAMPLE 5

CHECK

You wash 36 = 4 cars and your friend washes 36 = 3 cars in 36 minutes. Together, you wash 7 cars.

112

19

GUIDED PRACTICE for Examples 3, 4, and 5