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

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

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

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

- 2 < x < 0

Solution steps

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

Find positive and negative intervals

x < - 1, x \geq - 1

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 2 < x < 0

∣ x - 1 ∣ + ∣ x + 2 ∣ \geq 3

\frac{1}{( 2 - ∣ x ∣ )} \geq 1

x^{2} - 3 x - 3 > x^{2} + 7 x - 13

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

\frac{( ∣ x ∣ + 4 )}{( ∣ x ∣ + 3 )} \geq 0