What is x^2-|5x+6|>0 ?

The solution to x^2-|5x+6|>0 is x 6

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x^2-|5x+6|>0

x^{2} - ∣ 5 x + 6 ∣ > 0

x < - 3 or - 2 < x < - 1 or x > 6

Interval Notation

(- \infty, - 3) \cup (- 2, - 1) \cup (6, \infty)

Solution steps

x^{2} - ∣ 5 x + 6 ∣ > 0

Find positive and negative intervals

x < - \frac{6}{5}, x \geq - \frac{6}{5}

Solve the inequality for each interval

(x < - 3 or - 2 < x < - \frac{6}{5}) or (- \frac{6}{5} \leq x < - 1 or x > 6)

Merge Overlapping Intervals

x < - 3 or - 2 < x < - 1 or x > 6

x^{2} + 5 x < 6, ∣ x + 1 ∣ \leq 1

∣ 2 x - 1 ∣ > - 3

∣ 3 x - 4 ∣ \leq - 6

∣ 3 x - 2 ∣ > 1

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