What is |x+2|-|x-1|<x ?

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|x+2|-|x-1|<x

∣ x + 2 ∣ - ∣ x - 1 ∣ < x

- 3 < x < - 1 or x > 3

Interval Notation

(- 3, - 1) \cup (3, \infty)

Solution steps

∣ x + 2 ∣ - ∣ x - 1 ∣ < x

Find positive and negative intervals

x < - 2, - 2 \leq x < 1, x \geq 1

Solve the inequality for each interval

- 3 < x < - 2 or - 2 \leq x < - 1 or x > 3

Merge Overlapping Intervals

- 3 < x < - 1 or x > 3

∣ 5 x - 3 ∣ > - 3

d (∣ x - 3 ∣ - 2) > 1

\frac{4 x + 8}{8} > 3

9 ∣ y - 8 ∣ - 6 \geq 30

∣ (- 2 x + 9) (x - 1) ∣ < 5 ∣ x - 1 ∣