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**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

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**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.

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**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

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**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.

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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.

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**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.

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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

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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.

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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

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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.

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