ALGB-1-Solving Inequalities

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Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Inequalities
Solve each inequality and graph its solution.
Date________________ Period____
1) 0 > 3x − 3 − 6
2) 4x + 1 − 1 ≥ −8
−2 −1 0 1 2 3 4 5 6 7 8
−5 −4 −3 −2 −1 0 1
3) −1 ≤ 2n + 4 − 5
4) −6 > 5n + 5 + 4
−2 −1 0 1 2 3 4
−7 −6 −5 −4 −3 −2 −1 0 1 2
5) 0 ≤ 2n + 3n
6) 2p − 4 p ≤ −2
−5 −4 −3 −2 −1 0 1 2
−4 −3 −2 −1 0 1 2 3 4 5
7) 7 < −(−k − 3) + 2
8) 3 − 2(n − 4) > −1
−3 −2 −1 0 1 2 3 4
3 4 5 6 7 8
9) −5(1 − 4a) > −5
10) −2(b + 1) + 4 < 10
−4 −3 −2 −1 0 1 2 3 4
−8 −7 −6 −5 −4 −3 −2 −1 0 1

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11) a − 15 > −4(−6 + 3a)
12) 3(6b − 1) > 18 − 3b
1 2 3 4 5
−1 0 1 2 3 4 5
13) 26 + m ≥ 5(−6 + 3m)
14) 20 − 2p > −2( p + 2) + 4p
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9
15) x + 1 + 1 + 6x > 3(x − 4) − (x − 4)
16) −6(1 + 6x) < 6(1 − 5x)
−5 −4 −3 −2 −1 0 1 2 3
−6 −5 −4 −3 −2 −1 0 1 2
17) 2(1 − 4r) < −2(r + 3) − 4
18) −6(1 + 2x) ≥ 6(2x − 1) + 2x
−2 −1 0 1 2 3 4
−2 −1 0 1 2 3 4
19) −2(1 − 5x) > −(x + 1) − 1
20) 5x − (x + 2) > −5(1 + x) + 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−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.

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Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Inequalities
Solve each inequality and graph its solution.
Date________________ Period____
1) 0 > 3x − 3 − 6
2) 4x + 1 − 1 ≥ −8
−2 −1 0 1 2 3 4 5 6 7 8
−5 −4 −3 −2 −1 0 1
3) −1 ≤ 2n + 4 − 5
4) −6 > 5n + 5 + 4
−2 −1 0 1 2 3 4
−7 −6 −5 −4 −3 −2 −1 0 1 2
5) 0 ≤ 2n + 3n
6) 2p − 4 p ≤ −2
−5 −4 −3 −2 −1 0 1 2
−4 −3 −2 −1 0 1 2 3 4 5
7) 7 < −(−k − 3) + 2
8) 3 − 2(n − 4) > −1
−3 −2 −1 0 1 2 3 4
3 4 5 6 7 8
9) −5(1 − 4a) > −5
10) −2(b + 1) + 4 < 10
−4 −3 −2 −1 0 1 2 3 4
−8 −7 −6 −5 −4 −3 −2 −1 0 1

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11) a − 15 > −4(−6 + 3a)
12) 3(6b − 1) > 18 − 3b
1 2 3 4 5
−1 0 1 2 3 4 5
13) 26 + m ≥ 5(−6 + 3m)
14) 20 − 2p > −2( p + 2) + 4p
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9
15) x + 1 + 1 + 6x > 3(x − 4) − (x − 4)
16) −6(1 + 6x) < 6(1 − 5x)
−5 −4 −3 −2 −1 0 1 2 3
−6 −5 −4 −3 −2 −1 0 1 2
17) 2(1 − 4r) < −2(r + 3) − 4
18) −6(1 + 2x) ≥ 6(2x − 1) + 2x
−2 −1 0 1 2 3 4
−2 −1 0 1 2 3 4
19) −2(1 − 5x) > −(x + 1) − 1
20) 5x − (x + 2) > −5(1 + x) + 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−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: 2x ≥ x + 2
22) Name one particular solution to question #20.
Any number greater than zero. Ex: 4.7
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