What is |x-3|>|x^2-3| ?

The solution to |x-3|>|x^2-3| is -3<x<0\lor 1<x<2

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|x-3|>|x^2-3|

∣ x - 3 ∣ > x^{2} - 3

- 3 < x < 0 or 1 < x < 2

Solution steps

∣ x - 3 ∣ > x^{2} - 3

Find positive and negative intervals

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

Solve the inequality for each interval

- 3 < x \leq - 3 or (- 3 < x < 0 or 1 < x < 3) or 3 \leq x < 2 or No Solution

Merge Overlapping Intervals

- 3 < x < 0 or 1 < x < 2

∣ x ∣ + ∣ x - 2 ∣ \leq 6

∣ x - 1 ∣ \leq 1

∣ 3 x ∣ > 5

x^{2} - ∣ x ∣ - 2 > 0

\frac{x + 1}{3} > \frac{8}{3}