What is |x^3-x|<= x ?

The solution to |x^3-x|<= x is 0<= x<= sqrt(2)

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|x^3-x|<= x

x^{3} - x \leq x

0 \leq x \leq 2

Solution steps

x^{3} - x \leq x

Find positive and negative intervals

x < - 1, - 1 \leq x \leq 0, 0 < x < 1, x \geq 1

Solve the inequality for each interval

No Solution or x = 0 or 0 < x < 1 or 1 \leq x \leq 2

Merge Overlapping Intervals

0 \leq x \leq 2

\frac{1}{2} - \frac{( 5 x )}{3} \leq 5

\frac{( ∣ x + 2 ∣ + x )}{( x + 1 )} > 1

∣ x + 7 ∣ + ∣ x ∣ \leq \frac{1}{2}

x^{2} - 5 x + 6 < x^{2} - 2 x

x^{2} - 1 > 0