Worked-out Problems

Chapter 3 continued
38. ––CONTINUED––
b. 4(6x 8) 14
4(6x 8)
1 4
4 4
6x 8 3.5
6x 8 8 3.5 8
6x 11.5
6 x
11 .5
6 6
x 1 1 1
12
4(6x 8) 14
24x 32 14
24x 32 32 14 32
24x 46
2 4x
24
4 6
2
4
x 1 1 1
12
Sample answer: Both methods produce the same
answer. Divide first when the number outside the
parentheses is a factor of the constant on the other side
of the equation. This method will require fewer steps.
Distribute first when the number outside the parentheses
is not a factor of the constant on the other side of the
equation. This method will be easier because you are
working with integers.
39. Total area Area of triangle Area of rectangle
A 1 bh lw
2
1258 1 (3x 1)(24) (3x 1)(25)
2
1258 12(3x 1) (3x 1)(25)
1258 36x 12 75x 25
1258 111x 37
1258 37 111x 37 37
1221 111x
1 22
11
1
1
1 11x
1
11
11 x
3.2 Mixed Review (p. 129)
40–47.
Q
108 6
4
R
J y
8
6
4
N
2
P
2 4 6 8 x
M
K
4
L
6
8
40. Begin at the origin. Move 3 units to the left, then 8 units
up. Point J is located in Quadrant II.
41. Begin at the origin. Move 8 units to the right, then 3 units
down. Point K is located in Quadrant IV.
42. Begin at the origin. Move 4 units to the right, then 4 units
down. Point L is located in Quadrant IV.
43. Begin at the origin. Move 1 unit to the left, then 1 unit
down. Point M is located in Quadrant III.
44. Begin at the origin. Move 2 units up. Point N is located
on the y-axis.
45. Begin at the origin. Move 5 units to the right, then 1 unit
up. Point P is located in Quadrant I.
46. Begin at the origin. Move 9 units to the left. Point Q is
located on the x-axis.
47. Begin at the origin. Move 5 units to the left, then 8 units
down. Point R is located in Quadrant III.
48. a 2 (3 a) a 2 3 a
a a 2 3
0 5
5
49. 3b 8 2(b 4) 3b 8 2b 8
3b 2b 8 8
5b 0
5b
50. 2x 5 7(x 1) 2x 5 7x 7
2x 7x 5 7
9x (2)
9x 2
51. 2y 4 3(y 1) 2y 4 3y 3
2y 3y 4 3
5y 1
52. (2x 3) 4(x 2) 2x 3 4x 8
2x 4x 3 8
2x 5
53. 3(2x 7) 8(4 x) 6x 21 32 8x
6x 8x 21 32
2x 11
54. Let x the number of people.
Total Cost to Food cost Number
p
cost rent space per person of people
600 150 18x
600 150 150 18x 150
450 18x
4 50
1 8x
18
18
25 x
So, 25 people can come to the party.
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Chapter 3
Pre-Algebra 79
Worked-Out Solution Key