Download 5-5 Solving Multi-Step Equations and Inequalities

5-5 Solving Multi-Step Equations and Inequalities
Solve. Check your solution.
1. 4(x + 1) = 28
SOLUTION: Check:
2. 35 = 7(2p – 1)
SOLUTION: Check:
3. 2(a – 2) = 3(a – 5)
SOLUTION: Check:
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5-5 Solving Multi-Step Equations and Inequalities
3. 2(a – 2) = 3(a – 5)
SOLUTION: Check:
4. 16(z + 3) = 4(z + 9)
SOLUTION: Check:
5. 7(x + 2) = 2(x + 2)
SOLUTION: Check:
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5-5 Solving Multi-Step Equations and Inequalities
5. 7(x + 2) = 2(x + 2)
SOLUTION: Check:
6. 3(d – 2) = 5(d + 8)
SOLUTION: Check:
7. 6x + 4 = 2(3x – 5)
SOLUTION: The statement 4 = –10 is never true. The equation has no solutions and the solution set is
.
8. 20f + (–8f – 15) = 3(4f – 5)
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5-5 Solving Multi-Step Equations and Inequalities
The statement 4 = –10 is never true. The equation has no solutions and the solution set is
.
8. 20f + (–8f – 15) = 3(4f – 5)
SOLUTION: The statement –15 = –15 is always true. The equation is an identity and the solution set is all numbers.
9. 3(1 + 2f ) – 5 = 6f – 2
SOLUTION: The statement –2 = –2 is always true. The equation is an identity and the solution set is all numbers.
10. 7x + 5 = 10(x – 7) – 3x
SOLUTION: The statement 5 = –70 is never true. The equation has no solutions and the solution set is
.
11. MULTIPLE CHOICE You and three friends are going to the fair. The cost for parking is $5 per car and
admission to the fair is $19 per person. If you have a total of $113, how much can each person spend on food?
A. $4
B . $8
C. $12
D. $24
SOLUTION: Total Cost = parking + admission + food
Let x = the amount each person spends on food.
Then 19 + x is the amount each person spends.
Each person can spend $8 on food. Choice B is the correct answer.
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Solve. Check your solution.
18. 6n – 18 = 4(n + 2)
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5-5 Solving Multi-Step Equations and Inequalities
The statement 5 = –70 is never true. The equation has no solutions and the solution set is
.
11. MULTIPLE CHOICE You and three friends are going to the fair. The cost for parking is $5 per car and
admission to the fair is $19 per person. If you have a total of $113, how much can each person spend on food?
A. $4
B . $8
C. $12
D. $24
SOLUTION: Total Cost = parking + admission + food
Let x = the amount each person spends on food.
Then 19 + x is the amount each person spends.
Each person can spend $8 on food. Choice B is the correct answer.
Solve. Check your solution.
18. 6n – 18 = 4(n + 2)
SOLUTION: Check:
19. 12y + 5(y – 6) = 4
SOLUTION: Check:
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5-5 Solving Multi-Step Equations and Inequalities
19. 12y + 5(y – 6) = 4
SOLUTION: Check:
20. 12z + 4 = 2(5z + 8) – 12
SOLUTION: Check:
21. d – 12 = 4(d – 6)
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
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5-5 Solving Multi-Step Equations and Inequalities
21. d – 12 = 4(d – 6)
SOLUTION: Check:
22. 3x + 2 = 2(2x – 7)
SOLUTION: Check:
23. 6(y – 5) = 2(10 + 3y)
SOLUTION: The statement –30 = 20 is never true. The equation has no solutions and the solution set is
.
24. 4(2c + 8) = 5(c + 4)
SOLUTION: eSolutions Manual - Powered by Cognero
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5-5 Solving Multi-Step Equations and Inequalities
The statement –30 = 20 is never true. The equation has no solutions and the solution set is
.
24. 4(2c + 8) = 5(c + 4)
SOLUTION: Check:
25. 10 + 12p = 3(3 + 4p )
SOLUTION: The statement 10 = 9 is never true. The equation has no solutions and the solution set is
.
26. 3x + 2 + 5(x – 1) = 8x + 17
SOLUTION: The statement –3 = 17 is never true. The equation has no solutions and the solution set is
.
27. 10z + 4 = 2(5z + 8) – 12
SOLUTION: The statement 4 = 4 is always true. The equation is an identity and the solution set is all numbers.
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28. GEOMETRY The perimeter of a rectangle is 50 centimeters. The length of the rectangle is one more than 3 times
the width of the rectangle. What are the dimensions of the rectangle?
5-5 Solving Multi-Step Equations and Inequalities
The statement –3 = 17 is never true. The equation has no solutions and the solution set is
.
27. 10z + 4 = 2(5z + 8) – 12
SOLUTION: The statement 4 = 4 is always true. The equation is an identity and the solution set is all numbers.
28. GEOMETRY The perimeter of a rectangle is 50 centimeters. The length of the rectangle is one more than 3 times
the width of the rectangle. What are the dimensions of the rectangle?
SOLUTION: The perimeter of a rectangle is 50 centimeters.
Let w = the width of the rectangle.
The length of the rectangle is one more than 3 times the width of the rectangle.
So, the length l = 1 + 3w.
Use the formula for perimeter, P = 2l + 2w.
The width of the rectangle is 6 cm, and the length of the rectangle is 1 + 3(6), or 19 cm.
29. FINANCIAL LITERACY Tim is taking the train to Seattle to visit his grandparents. He was given $15 to spend
on snacks and reading material. Granola bars cost $1.15 each, and magazines cost $1.25. If Tim buys the same
number of granola bars and magazines, how many can he buy?
SOLUTION: Tim has at most $15 to spend on snacks and reading material.
Let x = the number of granola bars he buys.
Since Tim buys the same number of granola bars and magazines, then x = the number of magazines.
Each granola bar costs $1.15, and each magazine cost $1.25.
Tim can buy at most 6 granola bars and 6 magazines.
38. SCHOOL Nomar has earned scores of 73, 85, 91, and 82 on the first four of five math tests for the grading period.
He would like to finish the grading period with a test average of at least 82. What is the minimum score Nomar
needs to earn on the fifth test in order to achieve his goal?
SOLUTION: Nomar wants his average to be at least 82.
He earned scores of 73, 85, 91, and 82 on the first four tests.
Let s = his score on the fifth test.
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Each granola bar costs $1.15, and each magazine cost $1.25.
5-5 Solving Multi-Step Equations and Inequalities
Tim can buy at most 6 granola bars and 6 magazines.
38. SCHOOL Nomar has earned scores of 73, 85, 91, and 82 on the first four of five math tests for the grading period.
He would like to finish the grading period with a test average of at least 82. What is the minimum score Nomar
needs to earn on the fifth test in order to achieve his goal?
SOLUTION: Nomar wants his average to be at least 82.
He earned scores of 73, 85, 91, and 82 on the first four tests.
Let s = his score on the fifth test.
Nomar must score at least a 79 on the fifth test.
Solve.
39. –0.2(3c + 15) = 3(0.8c – 8)
SOLUTION: 40. 2(t + 12) – 6(2t – 3) = 14
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