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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 The correct answer is 4. for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. 5. –2x + 9 = 2x – 7 SOLUTION –2x + 9 = 2x – 7 Write original equation. –4x + 9 = – 7 Subtract 2xfrom each side. –4x = –16 subtract 9 from each side. x = 4 Divide each side by –4.

  9. –2(4) + 9 2(4) – 7 ? = for Examples 3, 4, and 5 GUIDED PRACTICE CHECK Substitute 4 for x. –8 + 9 = 8 – 7 Simplify 1 = 1 Solution check

  10. ANSWER The correct answer is 1. for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. 6. 10 – x = – 6x + 15 SOLUTION 10 – x = – 6x + 15 Write original equation. 10 + 5x = 15 Add 6xto each side. 5x = 5 subtract 10 from each side. x = 1 Divide each side by –5.

  11. 10 –1 – 6(1) + 15 ? = for Examples 3, 4, and 5 GUIDED PRACTICE CHECK Substitute 1 for x. 9 = 9 Solution check.

  12. ANSWER The solution is –7. for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. 7. 3(x + 2) = 5(x + 4) SOLUTION 3(x + 2) = 5(x + 4) Write original equation. 3x + 6 = 5x + 20 Distributive property. 6= 2x + 20 Subtract 3x from each side. – 14 = 2x Subtract 20 from each side. Solve for x x = –7

  13. 3((–7) + 2) 5 (–7 + 4) 3(–5) 5 (–3) ? ? = = for Examples 3, 4, and 5 GUIDED PRACTICE CHECK Substitute –7 for x. Simplify – 15 = –15 Solution check.

  14. for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. 8. – 4(2x + 5) = 2(– x – 9) – 4x SOLUTION – 4(2x + 5) = 2(–x – 9) – 4x Write original equation. –8x – 20 = –2x – 18 – 4x Distributive property. –8x – 20 = –6x – 18 Combine like term. –20 = 2x – 18 Add 8x to each side. –2 = 2x Add 18 to each side. x = –1 Divide each side by 2.

  15. –4 (2(–1) + 5 ) 2(–(–1) – 9) – 4(–1) – 4( – 2 + 5) 2 (– 8) + 4 – 4( 3) (–16) + 4 ANSWER The solution x =–1 ? ? ? = = = for Examples 3, 4, and 5 GUIDED PRACTICE CHECK Substitute –1 for x. Simplify. – 12 = –12 Solution checks.

  16. 9. x + x = 39 x + x = 39 1 2 1 13x 4 5 4 = 39 20 2 5 13x = 39 20 ANSWER The correct answer is 60 for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution. SOLUTION Write original equation. Combine like term. Multiply each side by 20. x = 60 Divide each side to 13.

  17. 1 (60) + (60) 39 4 x + x = 39 39 + 1 2 2 5 4 5 ? ? = = 120 60 5 4 for Examples 3, 4, and 5 GUIDED PRACTICE CHECK Write original equation. Substitute 60 for x. Simplify Solution checks.  39 = 39

  18. 1 5 10. x+ = x – 2 6 2 3 ANSWER The correct answer is 4 for Examples 3, 4, and 5 GUIDED PRACTICE Solve the equation. Check your solution.

  19. 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. 1 car 1 car tmin + tmin = 7 9 min 12 min for Examples 3, 4, and 5 GUIDED PRACTICE SOLUTION

  20. STEP 2 Solve the equation for t. 1 t + t = 7 12 36( t +t) = 36 (7) 1 12 1 9 1 9 It will take 36 minutes to wash 7 cars if you work together. ANSWER for Examples 3, 4, and 5 GUIDED PRACTICE Write equation. Multiply each side by the LCD, 24. 4t + 3t = 252 Distributive property 7t = 252 Combine like terms. t = 36 Divide each side by 7.

  21. 1 You wash 36 = 4 cars and your friend washes 36 = 3 cars in 36 minutes. Together, you wash 7 cars. 12 1 9 EXAMPLE 5 for Examples 3, 4, and 5 GUIDED PRACTICE CHECK

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