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EXAMPLE 3

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

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EXAMPLE 3

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

  2. 7(9) + 13 9(9) – 5 63 + 13 81 – 5 ? ? = = EXAMPLE 3 Standardized Test Practice CHECK 7p+ 13 = 9p– 5 Write original equation. Substitute 9 for p. Multiply. 76 = 76 Solution checks.

  3. x = 2 2 ANSWER The solution 5 5 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 10xto each side. 25x = 10 Add 24 to each side. Divide each side by 25 and simplify.

  4. 3(5 – 8) –2(– + 7) – 12 24 3(–6) –14 – 5 4 5 Substitute for x. 2 2 2 5 5 5 2 ? ? = = 5 EXAMPLE 4 Solve an equation using the distributive property CHECK Simplify. – 18 = – 18 Solution checks.

  5. 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? STEP 1 Write a verbal model. Then write an equation. EXAMPLE 5 Solve a work problem SOLUTION

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

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

  8. ANSWER ANSWER ANSWER The correct answer is 4. The correct answer is 1. The solution is –7. for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. 5. –2x + 9 = 2x – 7 6. 10 – x = –6x + 15 7. 3(x + 2) = 5(x + 4)

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

  10. 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. 1 5 10. x + = x – 2 6 2 3 It will take 36 minutes to wash 7 cars if you work together. ANSWER ANSWER The correct answer is 4 for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution.

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