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

The solution to |x^3-1|>= 1-x is x = 0

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|x^3-1|>= 1-x

x^{3} - 1 \geq 1 - x

x \leq - 1 or x \geq 0

Interval Notation

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

Solution steps

x^{3} - 1 \geq 1 - x

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

(x \leq - 1 or 0 \leq x < 1) or x \geq 1

Merge Overlapping Intervals

x \leq - 1 or x \geq 0

∣ x ∣ < 2

x^{2} - 2 x + 3 < - 3

\frac{1}{x - 2} < 4

∣ x - 5 ∣ + ∣ x + 4 ∣ \leq 7

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x + 1 ∣ > ∣ x + 2 ∣ + ∣ x ∣ - 3