SOLVING ABSOLUTE VALUE INEQUALITIES PRACTICE QUESTIONS

Solve the following absolute value inequalities

1) |3 - x| < 7

2) |4x - 5| > -2

3) |3 - (3x/4)| ≤ 1/4

4) |x| - 10 < -3

5) (1/|2x - 1|) < 6

6) -3|x| + 5 ≤ -2

7) 2|x + 1| - 6 ≤ 7

8) (1/5) |10x − 2| < 1

9) |5x - 12| < -2

10) |x| < 0

11) |x + 2| ≤ 3

12) |x - 3| ≥ 1

Answers :

1) Possible values of x : -4 < x < 10

Interval notation : (-4, 10)

2) All the real numbers.

3) Possible values of x : 11/3 ≤ x ≤ 13/3

Interval notation : [11/3, 13/3]

4) Possible values of x : -7 < x < 7

Interval notation : (-7, 7)

5) Possible values of x : x < 5/12 or x > 7/12

Interval notation : (-∞, 5/12) U (7/12, ∞)

6) Possible values of x : x ≤ -7/3 or x ≥ 7/3

Interval notation : (-∞, -7/3] U [7/3, ∞)

7) Possible values of x : -15/2 ≤ x ≤ 11/2

Interval notation : [-15/2, 11/2]

8) Possible values of x : -3/10 < x < 7/10

Interval notation : (-3/10, 7/10)

9) There is no solution.

10) There is no solution.

11) Possible values of x : -5 ≤ x ≤ 1

Interval notation : [-5, 1]

12) Possible values of x : x ≤ 2 or x ≥ 3

Interval notation : (-∞, 2] U [3, +∞)

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