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

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

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

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

Solve the equation for t. STEP 2 1 8 t + t = 7 6 24( t + t) = 24 (7) 1 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.

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. 1 6 8

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

Solve the equation. Check your solution. GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 6. 10 – x = – 6x + 15 SOLUTION 10 – x = – 6x + 15 Write original equation. 10 + 5x = 15 Add 6x to each side. 5x = 5 subtract 10 from each side. x = 1 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 = 10 –1 – 6(1) + 15 ? = Substitute 1 for x. 9 = 9 Solution check.

Solve the equation. Check your solution. 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) Write original equation. 3x + 6 = 5x + 20 Distributive property. 6 = 2x + 20 Subtract 3x from each side. – 14 = 2x Subtract 20 from each side. x = –7 Solve for x ANSWER The solution is –7.

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

Solve the equation. Check your solution. 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 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.

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

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

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

GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 10. x+ = x – 1 2 3 5 6 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. SOLUTION STEP 1 Write a verbal model. Then write an equation. t min 1 car 9 min 12 min t min = 7 +

Solve the equation for t. STEP 2 1 9 t + t = 7 12 36( t + t) = 36 (7) GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation for t. STEP 2 1 9 t + t = 7 12 Write equation. 36( t + t) = 36 (7) 1 9 12 Multiply each side by the LCD, 24. 4t + 3t = 252 Distributive property 7t = 252 Combine like terms. t = 36 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 You wash 36 = 4 cars and your friend washes 36 = 3 cars in 36 minutes. Together, you wash 7 cars. 1 12 9