Algebra Problems  10 - Solve Absolute Value Inequalities
 
A set of intermediate algebra problems, related solving inequalities with absolute value, are presented along with their answers. The solutions are at the bottom of the page. These questions may be used with the tutorials on how to Solve Inequalities With Absolute Value.

  1. Solve the following absolute value inequalities.

    a) | x | ≤ 3

    b) | x | ≥ 5

    c) | x | ≤ 0

    d) | x | < 0

    e) | x | ≥ 0

    f) | x | > 0

    g) | 2 x + 2 | ≤ 10

    h) | 3 x - 7 | ≤ 0

    i) | -x + 3 | ≥ 7

    j) | 3 x + 9 | > 0

    k) 2 | 4x - 10 | + 3 ≥ 17

    l) -3 | -5x + 2 | + 5 < -10

Answers to the Above Questions

a) [-3 , 3]

b) (-infinity , -5] U [5 , + infinity)

c) {0}

d) no solutions

e) (-ininity , + infinity)

f) (-ininity , 0) U (0 , + infinity)

g) [-6 , 4]

h) {7/3}

i) (-ininity , -4] U [10 , + infinity)

j) (-ininity , -3) U (-3 , + infinity)

k) (-ininity , 3/4] U [17/4 , + infinity)

k) (-ininity , -3/5] U [7/5 , + infinity)

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