Math 095–Review Sheet for Test #1–page 1
Simplify.
1.
8y + 19 + 2y ! 25
3.
18 + 3(2 ! 7)2 + 20 ÷ 2 @ 5
2.
2(4m ! 3) ! 5(2m ! 6)
Solve.
4.
k + 17 = 3
5.
z ! 25 = !8
6.
8a = !96
7.
2y ! 29 = !19
8.
8(2m ! 5) = !4(3m + 12)
9.
3x + 4 + 9x = 16
10.
13.
11.
3(4x + 2) = 6(2x + 5)
16.
12.
14.
8z + 12 = 2(4z + 6)
15.
17.
P = 2l + 2w; l = 8, w = 5
18.
Solve V = lwh for w
Set up and solve.
19.
When 5 is subtracted from three times a number, the result is the same as 11 added to twice the
number. Find the number.
20.
Garry spent $24 more than three times what Joe spent. Together they spent $196. How much did
each one spend?
21.
In a rectangle, the length is 8 inches more than the width. The perimeter is 44 inches. Find the
length and width.
22.
Use a proportion: If 3 inches on a map represents 171 miles, how many miles are represented by 5
inches on the map?
23.
How many liters of a 10% solution must be mixed with 40 liters of a 50% solution to get a 20%
solution?
24.
Mabel invested some money at 9% simple interest, and $5000 more than 3 times this amount at 10%.
She earned $2,840 in interest. How much did she invest at each rate?
25.
A club sold red shirts for $12 and white shirts for $9. If the club sold 40 shirts and made $396, how
many of each type of shirt was sold?
26.
Mary and Jane went biking. Mary biked at 8 mph and traveled north. Jane biked at 10 mph and
traveled south. How long was it until they were 63 miles apart?
Math 095–Review Sheet for Test #1–page 2
Solve. State solution in interval notation. (Graph the solution if needed.)
27.
x + 14 > 2
28.
!3x $ !18
29.
4x ! 20 > 20
30.
10(x + 3) < 2x + 4
31.
5x + 12 # 10x ! 24
32.
!8 < 2x + 10 # 32
33.
x > 3 and x # 10
34.
x > 8 or x # !4
35.
x + 3 # 7 and !4x < 8
36.
x ! 11 $ !25 or !2x + 1 > 17
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
Answer Key.
1.
10y ! 6
2.
!2m + 24
3.
143
4.
k = !14
5.
z = 17
6.
a = !12
7.
y= 5
8.
m=
9.
x= 1
10.
x=
11.
x=
12.
x=
13.
no solution
14.
all reals
15.
a= 6
16.
m=
17.
P = 26
18.
Math 095–Review Sheet for Test #1–page 3
19.
the number = x
3x ! 5 = 2x + 11
The number is 16.
20.
what Joe spent = x
what Garry spent = 3x + 24
Joe + Garry = 196
(x) + (3x + 24) = 196
Joe spent $43; Garry spent $153.
21.
width = x
22.
miles = x
length = x + 8
2l + 2w = P
2(x + 8) + 2(x) = 44
The width is 7 inches;
the length is 15 inches.
3x = 171(5)
285 miles are represented by 5 inches.
23.
liters of 10% solution = x
0.10(x) + 0.50(40) = 0.20(x + 40)
120 liters of 10% solution
24.
dollars invested at 9% = x
dollars invested at 10% = 3x + 5000
0.09(x) + 0.10(3x + 5000) = 2840
$6000 invested at 9%;
$23,000 invested at 10%
25.
red shirts = x
40 ! x = white shirts
26.
time = x
8x + 10x = 63
12(x) + 9(40 ! x) = 396
It took 3
hours.
12 red shirts; 28 white shirts
27.
x > !12
(!12, 4)
28.
x#6
(!4, 6]
29.
x > 10
30.
x<
32.
!9 < x # 11
(10, 4)
31.
x$
(!9, 11]
33.
34.
3 < x # 10
x # !4 or x > 8
Math 095–Review Sheet for Test #1–page 4
35.
!2 < x # 4
36.
all reals or
37.
{!7, 7}
x = !7 or x = 7
38.
{!13, 7}
x = !13 or x = 7
39.
40.
x < !9 or x > 9
41.
!10 # x # 10
42.
x # !34 or x $ 16
!6 < x < 10
43.
[!5, 9]
!5 # x # 9
44.
45.
empty set or i
46.
(!4, !15) c (4, 4)
x < !15 or x > 4
or all reals