What is |x^3-1|<= x^2+x+1 ?

The solution to |x^3-1|<= x^2+x+1 is 0<= x<= 2

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|x^3-1|<= x^2+x+1

x^{3} - 1 \leq x^{2} + x + 1

0 \leq x \leq 2

Solution steps

x^{3} - 1 \leq x^{2} + x + 1

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

0 \leq x < 1 or 1 \leq x \leq 2

Merge Overlapping Intervals

0 \leq x \leq 2

∣ 2 x ∣ + 4 > 0

∣ 2 x - 3 ∣ - ∣ x ∣ \leq 3

x^{2} - 5 x > x^{2} - ∣ 5 x ∣

∣ 2 x - 3 ∣ < ∣ x + 2 ∣

x^{2} - 3 x + 1 < 1