example 3
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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EXAMPLE 3 Standardized Test Practice
SOLUTION
7p + 13 = 9p – 5
13 = 2p – 5
18 = 2p
9 = p
Write original equation.
Subtract 7p from each side.
Add 5 to each side.
Divide each side by 2.
ANSWER The correct answer is D
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EXAMPLE 3 Standardized Test Practice
CHECK
7p + 13 = 9p – 5
7(9) + 13 9(9) – 5=?
63 + 13 81 – 5=?
76 = 76
Write original equation.
Substitute 9 for p.
Multiply.
Solution checks.
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EXAMPLE 4 Solve an equation using the distributive property
Solve 3(5x – 8) = – 2(– x + 7) – 12x.
3(5x – 8) = – 2(– x + 7) – 12x
15x – 24 = 2x – 14 – 12x
15x – 24 = – 10x – 14
25x – 24 = –14
25x = 10
x = 25
Write original equation.
Distributive property
Combine like terms.
Add 10x to each side.
Add 24 to each side.
Divide each side by 25 and simplify.
ANSWER The solution 25
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EXAMPLE 4 Solve an equation using the distributive property
CHECK
3 (5 – 8) – 2(– +7) – 12 25
25
25=?
3( – 6) –14 – 45=? 24
5
– 18 = – 18
25
Substitute for x.
Simplify.
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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EXAMPLE 5 Solve a work problem
Solve the equation for t.STEP 2
18
t + t = 716
24( t + t) = 24 (7)18
16
3t + 4t = 168
7t = 168
t = 24
Write equation.
Multiply each side by the LCD, 24.
Distributive property
Combine like terms.
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 24 = 3 cars and your friend washes 24 = 4 cars in 24 minutes. Together,
you wash 7 cars.
16
18
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GUIDED PRACTICE for Examples 3, 4, and 5
Solve the equation. Check your solution.
5. –2x + 9 = 2x – 7
SOLUTION
–2x + 9 = 2x – 7
–4x + 9 = – 7
–4x = –16
x = 4
Write original equation.
Subtract 2x from each side.
subtract 9 from each side.
Divide each side by –4.
ANSWER The correct answer is 4.
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GUIDED PRACTICE for Examples 3, 4, and 5
CHECK
–2(4) + 9 2(4) – 7?= Substitute 4 for x.
–8 + 9 = 8 – 7
1 = 1 Solution check
Simplify
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GUIDED PRACTICE for Examples 3, 4, and 5
Solve the equation. Check your solution.
6. 10 – x = – 6x + 15
SOLUTION
10 – x = – 6x + 15
10 + 5x = 15
5x = 5
x = 1
Write original equation.
Add 6x to each side.
subtract 10 from each side.
Divide each side by –5.
ANSWER The correct answer is 1.
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GUIDED PRACTICE for Examples 3, 4, and 5
CHECK
10 –1 – 6(1) + 15?= Substitute 1 for x.
9 = 9 Solution check.
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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)
3x + 6 = 5x + 20
6 = 2x + 20
x = –7
Write original equation.
Distributive property.
Subtract 3x from each side.
Solve for x
ANSWER The solution is –7.
– 14 = 2x Subtract 20 from each side.
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GUIDED PRACTICE for Examples 3, 4, and 5
CHECK
3((–7) + 2) 5 (–7 + 4)?= Substitute – 7 for x.
Solution check.
3(–5) 5 (–3)?=
– 15 = –15
Simplify
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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
SOLUTION
– 4(2x + 5) = 2(–x – 9) – 4x
–8x – 20 = –2x – 18 – 4x
–8x – 20 = –6x – 18
–20 = 2x – 18
Write original equation.
Distributive property.
Combine like term.
Divide each side by 2.x = –1
Add 8x to each side.
Add 18 to each side.–2 = 2x
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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.
Solution checks.
– 4( 3) (–16) + 4 =?
– 12 = –12
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GUIDED PRACTICE for Examples 3, 4, and 5
Solve the equation. Check your solution.
x + x = 3914
25
9.
SOLUTION
x = 60
Write original equation.
Combine like term.
Multiply each side by 20.
Divide each side to 13.
ANSWER The correct answer is 60
x + x = 3914
25
13x20
= 39
13x = 39 20
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CHECK
Write original equation.
Substitute 60 for x.
Simplify
Solution checks.
GUIDED PRACTICE for Examples 3, 4, and 5
14 (60) + (60) 392
5?=
?=120
5+ 604
39
39 = 39
x + x = 3914
25
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GUIDED PRACTICE for Examples 3, 4, and 5
Solve the equation. Check your solution.
10. x+ = x – 12
23
56
ANSWER The correct answer is 4
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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.
STEP 1 Write a verbal model. Then write an equation.
SOLUTION
t min1 car9 min
1 car12 min
t min = 7+
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Solve the equation for t.STEP 219
t + t = 7112
36( t + t) = 36 (7)19
112
4t + 3t = 252
7t = 252
t = 36
Write equation.
Multiply each side by the LCD, 24.
Distributive property
Combine like terms.
Divide each side by 7.
ANSWER It will take 36 minutes to wash 7 cars if you work together.
GUIDED PRACTICE for Examples 3, 4, and 5
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EXAMPLE 5
CHECK
You wash 36 = 4 cars and your friend washes 36 = 3 cars in 36 minutes. Together, you wash 7 cars.
112
19
GUIDED PRACTICE for Examples 3, 4, and 5