What is |x^2-2x-8|>2x ?

The solution to |x^2-2x-8|>2x is x 2sqrt(3)+2

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|x^2-2x-8|>2x

x^{2} - 2 x - 8 > 2 x

x < 22 or x > 23 + 2

Interval Notation

(- \infty, 22) \cup (23 + 2, \infty)

Decimal Notation

x < 2.82842 \dots or x > 5.46410 \dots

Solution steps

x^{2} - 2 x - 8 > 2 x

Find positive and negative intervals

x \leq - 2, - 2 < x < 4, x \geq 4

Solve the inequality for each interval

x \leq - 2 or - 2 < x < 22 or x > 23 + 2

Merge Overlapping Intervals

x < 22 or x > 23 + 2

3 ∣ 5 - 2 x ∣ > 7

∣ 7 x - 5 ∣ > - 2

x^{2} - 2 < 1

∣ 2 - 2 x ∣ < x^{2} - 3 x + 4

∣ - 2 x + 4 ∣ > - x + 8

What is |x^2-2x-8|>2x ?
The solution to |x^2-2x-8|>2x is x<2sqrt(2)\lor x>2sqrt(3)+2