Chapter 3 Test Review

Question 1

y + 24 = 15

Answer 1

y = -9

Question 2

82 = h - 17

Answer 2

h = 99

Question 3

c + 41 = 45

Answer 3

c = 4

Question 4

x - 32 = 10

Answer 4

x = 42

Question 5

1/14y = 12

Answer 5

y = 168

Question 6

-10v = -122

Answer 6

12.2

Question 7

-75 = 15x

Answer 7

x = -5

Question 8

-x/20 = 21

Answer 8

x = -420

Question 9

11y - 13 = 53

Answer 9

y = 6

Question 10

2/3x + 2 = 10

Answer 10

x = 12

Question 11

(4x + 70)/3 = 0

Answer 11

x = -17.5

Question 12

-1/2(w - 16) = 48

Answer 12

-1/2w + 8 = 48
-1/2w = 40
w = -80

Question 13

In the game of basketball, you can score one point for a foul shot, two points for a regular shot, and three points for an outside shot. Manuel scored 33 points by making eight foul shots and three outside shots. How many regular shots did he make? Use the 5-step plan.

Answer 13

2. x = regular shots
3. 33 = 1(8) + 2x + 3(3)
4. 33 = 8 + 2x + 9
   33 = 17 + 2x
   16 = 2x
   8 = x
5. 33 = 1(8) + 2(8) + 3(3)
   33 = 8 + 16 + 9
   33 = 24 + 9
   33 = 33

Question 14

8(a-6) = -3 + 6a

Answer 14

8a - 48 = -3 + 6a
2a = 45
a = 22.5

Question 15

8(m - 3) = 8(m + 4)

Answer 15

8m - 24 = 8m + 32
-24 = 32
No Solution; Empty Set

Question 16

Five times a number increased by 32 is the same as the opposite of the number. Find the number.

Answer 16

5n + 32 = -n
4n = -32
n = -8

Question 17

Sean weighs 20 lbs more than twice Brad’s weight. If Brad gains 20 lbs, together they’ll weigh 250 lbs. How much does each weigh now?

Answer 17

250 = 20 + 2b + b + 20
250 = 40 + 3b
210 = 3b
70 = b

Brad: 90 lb
Sean: 160 lb

Question 18

When Amy collected her change, she realized that she had 5 times as many dimes as quarters. Her dimes and quarters totaled $8.25. How many quarters did she have?

Answer 18

50x + 25x = 825
75x = 825
x = 11 quarters

Question 19

Prove: If ac = bc and c 0, then a = b
1. ac = bc
2. (ac) * 1/c = (bc) * 1/c
3. a(c * 1/c) = b(c * 1/c)
4. a * 1 = b * 1
5. a = b

Answer 19

1. Given
2. Multiplicative Property of Equality
3. Associative Property of Multiplication
4. Property of Reciprocals
5. Identity Property of Multiplication