What is |x^2-x-6|<x+2 ?

The solution to |x^2-x-6|<x+2 is 2<x<4

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|x^2-x-6|<x+2

x^{2} - x - 6 < x + 2

2 < x < 4

Interval Notation

(2, 4)

Solution steps

x^{2} - x - 6 < x + 2

Find positive and negative intervals

x \leq - 2, - 2 < x < 3, x \geq 3

Solve the inequality for each interval

No Solution or 2 < x < 3 or 3 \leq x < 4

Merge Overlapping Intervals

2 < x < 4

x^{2} + x < 2

∣ x - 3 ∣ < 2 ∣ x - 5 ∣

∣ x + 2 ∣ - ∣ x - 1 ∣ < x

∣ 5 x - 3 ∣ > - 3

d (∣ x - 3 ∣ - 2) > 1