EXAMPLE 3 Standardized Test Practice SOLUTION 7 p

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 9=p Add 5 to each side. Divide each side by 2. ANSWER The correct answer is D

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

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

EXAMPLE 4 Solve an equation using the distributive property CHECK ( 3 5 ) ( 2 – 8 ? – 2 +7 = 5 5 3( – 6) =? 4 – 14 – 24 5 5 – 18 = – 18 ) 2 for x. 2 Substitute – 12 5 5 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 STEP 2 1 t+ 8 24 1 t + 1 8 6 ( Solve a work problem Solve the equation for t. 1 t=7 Write equation. 6 t = 24 (7) Multiply each side by the LCD, 24. ) 3 t + 4 t = 168 Distributive property 7 t = 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.

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

GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 5. – 2 x + 9 = 2 x – 7 SOLUTION – 2 x + 9 = 2 x – 7 Write original equation. – 4 x + 9 = – 7 Subtract 2 x from each side. – 4 x = – 16 x=4 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 – 8 + 9 = 8 – 7 1=1 Substitute 4 for x. Simplify Solution check

GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 6. 10 – x = – 6 x + 15 SOLUTION 10 – x = – 6 x + 15 10 + 5 x = 15 5 x = 5 x=1 Write original equation. Add 6 x 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 9=9 Substitute 1 for x. 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) 3 x + 6 = 5 x + 20 6 = 2 x + 20 – 14 = 2 x x = – 7 Write original equation. Distributive property. Subtract 3 x from each side. Subtract 20 from each side. Solve for x ANSWER The solution is – 7.

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

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

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. – 4( 3) =? (– 16) + 4 – 12 = – 12 Solution checks.

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

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

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

GUIDED PRACTICE for Examples 3, 4, and 5 11. 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? SOLUTION STEP 1 Write a verbal model. Then write an equation. 1 car 9 min t min + 1 car 12 min t min = 7

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

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