SOLVING RATIONAL INEQUALITIES ALGEBRAICALLY PRACTICE QUESTIONS

Solve the following rational inequalities

1) (x + 2)/(x – 3) < 0

2) (x + 3)/(2 – x) < 0

3) (x - 1)/(x + 3) ≥ -1

4) (x + 2)/(2x - 3) < 1

5) (5 – 2x)/(1 - x) > 4

6) 4/x ≤ x

7) 3/x > 2/(x + 2)

8) x/(x + 6) > 3/x

9) (2x + 4)/(x - 1) ≥ 5

10) (x - 2)/(x + 5) > 2

Answers :

1) Possible values of x : -2 < x < 3

Interval notation : (-2, 3)

2) Possible values of x : x < -3 or x > 2

Interval notation : (-∞, -3) u (2, ∞)

3) Possible values of x : x < -3 or x ≥ -1

Interval notation : (-∞, -3) u [-1, ∞)

4) Possible values of x : x < 3/2 or x > 5

Interval notation : (-∞, 3/2) u (5, ∞)

5) Possible values of x : -1/2 < x < 1

Interval notation : (-1/2, 1)

6) Possible values of x : -2 ≤ x < 0 or x ≥ 2

Interval notation : [-2, 0) u [2, ∞)

7) Possible values of x : -6 < x < -2 or x > 0

Interval notation : (-6, -2) u (0, ∞)

8) Possible values of x : x < -6 or -3 < x < 0 or x > 6

Interval notation : (-∞, -6) u (-3, 0) u (6, ∞)

9) Possible values of x : 1 < x ≤ 3

Interval notation : (1, 3]

10) Possible values of x : -12 < x < -5

Interval notation : (-12, -5).

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