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Math Problems
Grade 8
Solve multi-step inequalities
Solve for
x
x
x
.
\newline
Your answer must be simplified.
\newline
x
−
15
≤
−
6
x-15 \leq-6
x
−
15
≤
−
6
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Solve for
x
x
x
.
\newline
Your answer must be simplified.
\newline
−
x
<
−
29
-x<-29
−
x
<
−
29
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Solve for
x
x
x
.
\newline
Your answer must be simplified.
\newline
−
18
<
9
x
-18<9 x
−
18
<
9
x
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Solve for
x
x
x
.
\newline
Your answer must be simplified.
\newline
−
3
<
x
−
10
-3<x-10
−
3
<
x
−
10
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Solve for
x
x
x
.
\newline
Your answer must be simplified.
\newline
17
x
>
−
17
17 x>-17
17
x
>
−
17
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Solve the exponential equation for
x
x
x
.
\newline
3
7
−
2
x
=
(
1
27
)
−
8
x
=
□
\begin{array}{l} 3^{7-2 x}=\left(\frac{1}{27}\right)^{-8} \\ x=\square \end{array}
3
7
−
2
x
=
(
27
1
)
−
8
x
=
□
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Solve the exponential equation for
x
x
x
.
\newline
5
7
x
+
5
=
12
5
2
x
−
7
x
=
□
\begin{array}{l} 5^{7 x+5}=125^{2 x-7} \\ x=\square \end{array}
5
7
x
+
5
=
12
5
2
x
−
7
x
=
□
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Solve the exponential equation for
x
x
x
.
\newline
7
−
9
x
+
1
=
4
9
−
12
x
=
□
\begin{array}{l} 7^{-9 x+1}=49^{-12} \\ x=\square \end{array}
7
−
9
x
+
1
=
4
9
−
12
x
=
□
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Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a
(
7.50
(7.50
(
7.50
delivery fee and
)
14
)14
)
14
per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under
$
60
\$60
$60
. Each pizza is cut into
8
8
8
slices, and she wonders how many total slices she can afford. Let
P
P
P
represent the number of pizzas that Jacque buys.
\newline
Which inequality describes this scenario?
\newline
Choose
1
1
1
answer:
\newline
(A)
7.50
+
14
P
<
60
7.50+14P < 60
7.50
+
14
P
<
60
\newline
(B)
7.50
+
14
P
>
60
7.50+14P > 60
7.50
+
14
P
>
60
\newline
(C)
14
+
7.50
P
<
60
14+7.50P < 60
14
+
7.50
P
<
60
\newline
(D)
14
+
7.50
P
>
60
14+7.50P > 60
14
+
7.50
P
>
60
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Solve for
d
d
d
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
38
d
−
57
≥
−
19
d
+
76
-38d-57 \geq -19d+76
−
38
d
−
57
≥
−
19
d
+
76
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Solve for
p
p
p
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
31
p
+
79
>
−
59
p
+
81
-31p + 79 > -59p + 81
−
31
p
+
79
>
−
59
p
+
81
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Solve for
b
b
b
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
67
b
+
6
≤
9
b
+
43
-67b + 6 \leq 9b + 43
−
67
b
+
6
≤
9
b
+
43
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Solve for
t
t
t
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
48
t
+
2
≤
−
71
t
+
14
-48t + 2 \leq -71t + 14
−
48
t
+
2
≤
−
71
t
+
14
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Solve for
y
y
y
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
5
y
+
3
>
−
7
y
+
13
5y + 3 > -7y + 13
5
y
+
3
>
−
7
y
+
13
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Solve for
x
x
x
.
\newline
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
4
x
+
4
≤
9
x
+
8
4x+4 \leq 9x+8
4
x
+
4
≤
9
x
+
8
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Solve for
q
q
q
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
50
q
+
43
>
−
11
q
+
70
50q + 43 > -11q + 70
50
q
+
43
>
−
11
q
+
70
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Solve for
c
c
c
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
55
c
+
13
≤
75
c
+
39
55c + 13 \leq 75c + 39
55
c
+
13
≤
75
c
+
39
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Solve for
y
y
y
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
65
y
+
19
<
−
2
y
+
41
-65y + 19 < -2y + 41
−
65
y
+
19
<
−
2
y
+
41
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Solve for
a
a
a
.
\newline
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
60
a
+
64
≥
80
a
−
92
60a+64 \geq 80a-92
60
a
+
64
≥
80
a
−
92
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Solve for
z
z
z
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
4
z
+
31
≥
17
z
+
23
-4z + 31 \geq 17z + 23
−
4
z
+
31
≥
17
z
+
23
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Solve for
n
n
n
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
64
n
−
6
≥
36
n
−
16
64n - 6 \geq 36n - 16
64
n
−
6
≥
36
n
−
16
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Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least
50
50
50
total rooms.
\newline
Joe had already reserved and paid for
16
16
16
rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains
8
8
8
rooms and costs
$
900
\$900
$900
.
\newline
Let
B
B
B
represent the number of additional blocks that Joe reserves.
\newline
Which inequality describes this scenario?
\newline
Choose
1
1
1
answer:
\newline
(A)
16
+
8
B
≤
50
16+8B \leq 50
16
+
8
B
≤
50
\newline
(B)
16
+
8
B
≥
50
16+8B \geq 50
16
+
8
B
≥
50
\newline
(C)
16
+
B
≤
50
16+B \leq 50
16
+
B
≤
50
\newline
(D)
16
+
B
≥
50
16+B \geq 50
16
+
B
≥
50
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Solve for
q
q
q
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
22
q
+
73
>
52
q
+
63
22q + 73 > 52q + 63
22
q
+
73
>
52
q
+
63
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Solve for
c
c
c
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
32
c
+
12
≤
−
66
c
−
16
-32c + 12 \leq -66c - 16
−
32
c
+
12
≤
−
66
c
−
16
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Solve for
r
r
r
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
35
r
−
21
<
−
35
r
+
19
35r-21 < -35r+19
35
r
−
21
<
−
35
r
+
19
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Solve for
x
x
x
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
54
x
+
64
≥
49
x
+
59
54x + 64 \geq 49x + 59
54
x
+
64
≥
49
x
+
59
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Solve for
w
w
w
.\ Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
53
w
+
13
<
56
w
+
16
53w+13 < 56w+16
53
w
+
13
<
56
w
+
16
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Solve for
p
p
p
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
7
p
−
4
>
26
p
−
94
-7p - 4 > 26p - 94
−
7
p
−
4
>
26
p
−
94
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Solve for
d
d
d
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
23
d
+
81
≤
−
98
d
+
1
-23d + 81 \leq -98d + 1
−
23
d
+
81
≤
−
98
d
+
1
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Solve for
b
b
b
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
30
b
+
53
≥
18
b
−
83
30b + 53 \geq 18b - 83
30
b
+
53
≥
18
b
−
83
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Solve for
t
t
t
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
4
t
−
3
>
37
t
−
50
4t-3 > 37t-50
4
t
−
3
>
37
t
−
50
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Solve for
v
v
v
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
42
v
+
33
<
8
v
+
91
-42v + 33 < 8v + 91
−
42
v
+
33
<
8
v
+
91
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Solve for
m
m
m
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
8
m
+
95
<
−
87
m
+
5
8m + 95 < -87m + 5
8
m
+
95
<
−
87
m
+
5
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Solve for
t
t
t
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
12
t
−
2
<
−
5
t
+
36
12t - 2 < -5t + 36
12
t
−
2
<
−
5
t
+
36
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Solve for
w
w
w
.
\newline
w
−
1
+
7
>
9
\frac{w}{-1} + 7 > 9
−
1
w
+
7
>
9
\newline
______
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