What is |x^3-1|>1-x ?

The solution to |x^3-1|>1-x is x 1

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|x^3-1|>1-x

x^{3} - 1 > 1 - x

x < - 1 or 0 < x < 1 or x > 1

Interval Notation

(- \infty, - 1) \cup (0, 1) \cup (1, \infty)

Solution steps

x^{3} - 1 > 1 - x

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

(x < - 1 or 0 < x < 1) or x > 1

Merge Overlapping Intervals

x < - 1 or 0 < x < 1 or x > 1

∣ x + 5 ∣ \geq ∣ 5 x - 7 ∣

1 - \frac{x - 2}{x} < - 3

∣ x + 1 ∣ > x - 3

∣ 2 x - 3 ∣ < x + 1

x^{2} - 4 x < 5, ∣ x + 1 ∣ < 3