m3
•
Study Guide and Review - Chapter 2
times
•
x
x
plus
+
three
3
equals
=
fifteen
15
SOLUTION: 3
three
p
p
+
plus
8
eight
=
equals
20
twenty
2
13. h – 5h + 6 = 0
SOLUTION: 10. Four times the difference of b and six is equal to b
squared.
SOLUTION: Rewrite the verbal sentence so it is easier to
translate. Four times the difference of b and six is
equal to b squared is the same as four times b
minus six equals b squared.
times
•
•
times
Three times p plus eight equals twenty can be
rewritten as the sum of three times p and eight is
the same as twenty.
The equation is 5x + 3 = 15.
four
4
9
Translate each equation into a sentence.
12. 3p + 8 = 20
SOLUTION: Rewrite the verbal sentence so it is easier to
translate. The sum of five times a number x and
three is the same as fifteen is the same as five
times x plus three equals fifteen.
five
5
–
= 4m – 9.
The equation is
Translate each sentence into an equation.
9. The sum of five times a number x and three is the
same as fifteen.
m
4m
=
b minus six
b–6
equals
=
b squared
b2
h2
–
h
squared
minus
5h
+
6
=0
five
times h
plus
6
equals
zero
h squared minus five times h plus six is equal to zero.
14. +
–
= 2
SOLUTION: 2
+
The equation is 4(b – 6) = b .
11. One half of m cubed is the same as four times m
minus nine.
SOLUTION: Rewrite the verbal sentence so it is easier to
translate. One half of m cubed is the same as four
times m minus nine is the same as one half times m
cubed equals four times m minus nine.
one
half
times
m
cubed
equals
•
m3
=
four
times
m
4m
minus
nine
–
9
Translate each equation into a sentence.
12. 3p + 8 = 20
SOLUTION: 3
three
•
times
p
p
+
plus
8
eight
=
equals
plus
two
thirds
w
minus
one
fifth
2
equals
two
Three-fourths w squared plus two-thirds w minus
one-fifth is equal to two.
15. FENCING Adrianne wants to create an outdoor
rectangular kennel. The length will be three feet
more than twice the width. Write and use an
equation to find the length and the width of the
kennel if Adrianne has 54 feet of fencing.
SOLUTION: To write the equation, let l stand for length and w
stand for width. Write an equation for l based on w: l
= 2w + 3.
Then substitute 2w + 3 for l into the formula for
perimeter.
= 4m – 9.
The equation is
three
fourths
w
squared
=
20
twenty
Three times p plus eight equals twenty can be
rewritten
the sumbyof
three times p and eight is
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the same as twenty.
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w
squared
plus
thirds
w
one
fifth
equals
two
Three-fourths
w squared
plus two-thirds
w minus
Study
Guide and Review
- Chapter
2
one-fifth is equal to two.
15. FENCING Adrianne wants to create an outdoor
rectangular kennel. The length will be three feet
more than twice the width. Write and use an
equation to find the length and the width of the
kennel if Adrianne has 54 feet of fencing.
SOLUTION: To write the equation, let l stand for length and w
stand for width. Write an equation for l based on w: l
= 2w + 3.
Then substitute 2w + 3 for l into the formula for
perimeter.
17. –6 + g = –11
SOLUTION: Check:
18. SOLUTION: Check:
Solve for l when w = 8.
The width is 8 feet and the length is 19 feet.
19. 3.8 = m + 1.7
SOLUTION: Solve each equation. Check your solution.
16. x – 9 = 4
SOLUTION: Check:
Check:
20. SOLUTION: 17. –6 + g = –11
SOLUTION: Check:
Check:
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21. 8y = 48
Check:
Study Guide and Review - Chapter 2
20. 23. SOLUTION: SOLUTION: Check:
Check:
21. 8y = 48
SOLUTION: 24. AGE Max is four years younger than his sister
Brenda. Max is 16 years old. Write and solve an
equation to find Brenda’s age.
Check:
22. SOLUTION: Let x be Brenda's age. Since Max is 4 years
younger, Max's age is x – 4 = 16.
Using this equation we can solve for Brenda's age: x
= 16 + 4 = 20. Brenda is 20 years old.
Solve each equation. Check your solution.
25. 2d – 4 = 8
SOLUTION: Check:
SOLUTION: Check:
26. –9 = 3t + 6
SOLUTION: 23. SOLUTION: eSolutions Manual - Powered by Cognero
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Study Guide and Review - Chapter 2
26. –9 = 3t + 6
28. SOLUTION: SOLUTION: Check:
Check:
27. 14 = –8 –2k
SOLUTION: 29. SOLUTION: Check:
Check:
28. SOLUTION: 30. SOLUTION: Check:
Check:
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29. SOLUTION: Page 4
Study Guide and Review - Chapter 2
30. 32. 0.2c + 4 = 6
SOLUTION: SOLUTION: Check:
Check:
33. SOLUTION: 31. 6g – 3.5 = 8.5
SOLUTION: Check:
Check:
34. 32. 0.2c + 4 = 6
SOLUTION: SOLUTION: Check:
Check:
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33. Page 5
Study Guide and Review - Chapter 2
34. SOLUTION: The consecutive odd numbers are 19, 21, and 23.
36. CONSECUTIVE INTEGERS Find three
consecutive integers with a sum of –39.
SOLUTION: To write an equation, let x, (x + 1), and (x + 2)
represent the three consecutive integers. Then, set
the sum of the integers equal to –39.
Check:
The consecutive integers are –12, –13, and –14.
Solve each equation. Check your solution.
37. 8m + 7 = 5m + 16
SOLUTION: 35. CONSECUTIVE INTEGERS Find three
consecutive odd integers with a sum of 63.
SOLUTION: To write an equation, let x, (x + 2), and (x + 4)
represent the three consecutive odd integers. Then,
set the sum of the integers equal to 63.
Check:
The consecutive odd numbers are 19, 21, and 23.
36. CONSECUTIVE INTEGERS Find three
consecutive integers with a sum of –39.
38. 2h – 14 = –5h
SOLUTION: SOLUTION: To write an equation, let x, (x + 1), and (x + 2)
represent the three consecutive integers. Then, set
the sum of the integers equal to –39.
Check:
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Study Guide and Review - Chapter 2
38. 2h – 14 = –5h
40. SOLUTION: SOLUTION: Check:
Check:
39. 21 + 3j = 9 – 3j
SOLUTION: 41. SOLUTION: Check:
Check:
40. SOLUTION: 42. 3(p + 4) = 33
Check:
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SOLUTION: Page 7
Study Guide and Review - Chapter 2
42. 3(p + 4) = 33
44. 4(3w – 2) = 8(2w + 3)
SOLUTION: SOLUTION: Check:
Check:
43. –2(b – 3) – 4 = 18
SOLUTION: Check:
44. 4(3w – 2) = 8(2w + 3)
SOLUTION: Check:
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