Infinite Algebra 1 - Compound Inequalities - Rancho High School

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Compound Inequalities

Date________________ Period____

Solve each compound inequality and graph its solution.

1) 7k + 8 ? 36 or 8 - 4k > 40

2) -14 ? 2x - 8 < -2

-10 -8 -6 -4 -2 0 2 4 6

k ? 4 or k < -8

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8

-3 ? x < 3

3) -69 < 8m - 5 ? 59

-10 -8 -6 -4 -2 0 2 4 6 8 10

-8 < m ? 8

4) 5m - 6 < -6 or -1 - 4m ? -21

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

m < 0 or m ? 5

5) 25 ? -7n - 3 < 39

-12 -10 -8

-6

-4

-2

0

-6 < n ? -4

6) 4n + 5 ? 21 or 3 - 8n ? -5

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8

n ? 4 or n ? 1

7) 5 - 4x ? 13 or 6 + 5x ? 31

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

x ? -2 or x ? 5

8) -2 + k ? 5 and 5 - 5k < 30

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

-5 < k ? 7

9) 8r - 7 < -39 or 6r - 1 > 41

-6 -4 -2 0 2 4 6 8 10

r < -4 or r > 7

10) -7 ? 4x - 7 ? 9

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

0 ? x ? 4

Worksheet by Kuta Software LLC

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11) -3 < -m - 8 ? -2

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

-6 ? m < -5

12) 7 + 2x > 7 or -8 - 6x ? 40

-10 -8 -6 -4 -2 0

2

x > 0 or x ? -8

13) 7a + 6 ? 27 or 7a - 5 < 2

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

a ? 3 or a < 1

14) 3v + 3 < 9 and -3 + 4v ? -23

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

-5 ? v < 2

15) -31 ? 6r + 5 < 17

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

-6 ? r < 2

16) -1 < 7 - 8m < 71

-10 -8 -6 -4 -2

0

2

-8 < m < 1

REVIEW: Solve each inequality and graph its solution.

17) 5(r - 8) ? -7 + 4(r - 5)

18) -2x + 6(x - 2) > 2(8 + x)

9 10 11 12 13 14 15 16 17 18 19

r ? 13

10 11 12 13 14 15 16 17 18 19 20

x > 14

Solve each inequality and graph its solution.

4 + x 19) 1 >

9

-2 -1 0 1 2 3 4 5 6 7 8

x < 5

3 + n

20)

< 2

6

7 8 9 10 11 12 13 14 15 16 17

n < 9

Evaluate each expression.

21) (4 + 1)2 - (1 + 5) ? 3

7

22) 4 + 4 ? 22 - 4 ? 2 12

Worksheet by Kuta Software LLC

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