What is x^2+2|x-3|-9>0 ?

The solution to x^2+2|x-3|-9>0 is x 3

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x^2+2|x-3|-9>0

x^{2} + 2 ∣ x - 3 ∣ - 9 > 0

x < - 1 or x > 3

Interval Notation

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

Solution steps

x^{2} + 2 ∣ x - 3 ∣ - 9 > 0

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

x < - 1 or x > 3

16 x^{2} + 24 x y + 9 y^{2}

x^{4} y^{3} \cdot (2 y^{2})^{0}

x^{2} - 3 x = (x + 3) (x - 4)

∣ x - 6 ∣ > 7

- x + 3 \geq 1 or 6 x + 4 < - 3