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

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

∣ x - 1 ∣ < x^{2} + 1

x < - 1 or x > 0

Interval Notation

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

Solution steps

∣ x - 1 ∣ < x^{2} + 1

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

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

Merge Overlapping Intervals

x < - 1 or x > 0

x^{3} - x \leq x

\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