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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Solving Inequalities
Solve each inequality and graph its solution.
1) 0 >
3
x
− 3 − 6
−2 −1 0 1 2 3 4 5 6 7 8
2)
4
x
+ 1 − 1 ≥ −8
−5 −4 −3 −2 −1 0 1
3) −1 ≤
2
n
+ 4 − 5
−2 −1 0 1 2 3 4
4) −6 >
5
n
+ 5 + 4
−7 −6 −5 −4 −3 −2 −1 0 1 2
5) 0 ≤
2
n
+ 3
n
−5 −4 −3 −2 −1 0 1 2
6)
2
p
− 4
p
≤ −2
−4 −3 −2 −1 0 1 2 3 4 5
7) 7 <
−
(
−
k
− 3
)
+ 2
−3 −2 −1 0 1 2 3 4
8)
3 −
2
(
n
− 4
)
> −1
3 4 5 6 7 8
9)
−5
(
1 − 4
a
)
> −5
−4 −3 −2 −1 0 1 2 3 4
10)
−2
(
b
+ 1
)
+ 4 < 10
−8 −7 −6 −5 −4 −3 −2 −1 0 1
-1-
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Worksheet by Kuta Software LLC
11)
a
− 15 >
−4
(
−6 + 3
a
)
1 2 3 4 5
12)
3
(
6
b
− 1
)
>
18 −
3
b
−1 0 1 2 3 4 5
13)
26 +
m
≥
5
(
−6 + 3
m
)
0 1 2 3 4 5 6 7
14)
20 −
2
p
>
−2
(
p
+ 2
)
+ 4
p
1 2 3 4 5 6 7 8 9
15)
x
+ 1 + 1 + 6
x
>
3
(
x
− 4
)
−
(
x
− 4
)
−5 −4 −3 −2 −1 0 1 2 3
16)
−6
(
1 + 6
x
)
<
6
(
1 − 5
x
)
−6 −5 −4 −3 −2 −1 0 1 2
17)
2
(
1 − 4
r
)
<
−2
(
r
+ 3
)
− 4
−2 −1 0 1 2 3 4
18)
−6
(
1 + 2
x
)
≥
6
(
2
x
− 1
)
+ 2
x
−2 −1 0 1 2 3 4
19)
−2
(
1 − 5
x
)
>
−
(
x
+ 1
)
− 1
−5 −4 −3 −2 −1 0 1 2 3 4 5
20)
5
x
−
(
x
+ 2
)
>
−5
(
1 +
x
)
+ 3
−3 −2 −1 0 1 2
Critical thinking questions:
21) Write an inequality with
x
on both sides whose
solution is
x
≥ 2
22) Name one particular solution to question #20.
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Solving Inequalities
Solve each inequality and graph its solution.
1) 0 >
3
x
− 3 − 6
−2 −1 0 1 2 3 4 5 6 7 8
2)
4
x
+ 1 − 1 ≥ −8
−5 −4 −3 −2 −1 0 1
3) −1 ≤
2
n
+ 4 − 5
−2 −1 0 1 2 3 4
4) −6 >
5
n
+ 5 + 4
−7 −6 −5 −4 −3 −2 −1 0 1 2
5) 0 ≤
2
n
+ 3
n
−5 −4 −3 −2 −1 0 1 2
6)
2
p
− 4
p
≤ −2
−4 −3 −2 −1 0 1 2 3 4 5
7) 7 <
−
(
−
k
− 3
)
+ 2
−3 −2 −1 0 1 2 3 4
8)
3 −
2
(
n
− 4
)
> −1
3 4 5 6 7 8
9)
−5
(
1 − 4
a
)
> −5
−4 −3 −2 −1 0 1 2 3 4
10)
−2
(
b
+ 1
)
+ 4 < 10
−8 −7 −6 −5 −4 −3 −2 −1 0 1
-1-
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Worksheet by Kuta Software LLC
11)
a
− 15 >
−4
(
−6 + 3
a
)
1 2 3 4 5
12)
3
(
6
b
− 1
)
>
18 −
3
b
−1 0 1 2 3 4 5
13)
26 +
m
≥
5
(
−6 + 3
m
)
0 1 2 3 4 5 6 7
14)
20 −
2
p
>
−2
(
p
+ 2
)
+ 4
p
1 2 3 4 5 6 7 8 9
15)
x
+ 1 + 1 + 6
x
>
3
(
x
− 4
)
−
(
x
− 4
)
−5 −4 −3 −2 −1 0 1 2 3
16)
−6
(
1 + 6
x
)
<
6
(
1 − 5
x
)
−6 −5 −4 −3 −2 −1 0 1 2
17)
2
(
1 − 4
r
)
<
−2
(
r
+ 3
)
− 4
−2 −1 0 1 2 3 4
18)
−6
(
1 + 2
x
)
≥
6
(
2
x
− 1
)
+ 2
x
−2 −1 0 1 2 3 4
19)
−2
(
1 − 5
x
)
>
−
(
x
+ 1
)
− 1
−5 −4 −3 −2 −1 0 1 2 3 4 5
20)
5
x
−
(
x
+ 2
)
>
−5
(
1 +
x
)
+ 3
−3 −2 −1 0 1 2
Critical thinking questions:
21) Write an inequality with
x
on both sides whose
solution is
x
≥ 2
Many answers. Ex: 2
x
≥
x
+ 2
22) Name one particular solution to question #20.
Any number greater than zero. Ex: 4.7
-2-
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