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

The solution to |x^2-1|<|x| is (-sqrt(5)-1)/2 <x<(-sqrt(5)+1)/2 \lor (sqrt(5)-1)/2 <x<(sqrt(5)+1)/2

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|x^2-1|<|x|

x^{2} - 1 < ∣ x ∣

\frac{- 5 - 1}{2} < x < \frac{- 5 + 1}{2} or \frac{5 - 1}{2} < x < \frac{5 + 1}{2}

Interval Notation

(\frac{- 5 - 1}{2}, \frac{- 5 + 1}{2}) \cup (\frac{5 - 1}{2}, \frac{5 + 1}{2})

Decimal Notation

- 1.61803 \dots < x < - 0.61803 \dots or 0.61803 \dots < x < 1.61803 \dots

Solution steps

x^{2} - 1 < ∣ x ∣

Find positive and negative intervals

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

Solve the inequality for each interval

\frac{- 5 - 1}{2} < x \leq - 1 or - 1 < x < \frac{- 5 + 1}{2} or \frac{5 - 1}{2} < x < 1 or 1 \leq x < \frac{5 + 1}{2}

Merge Overlapping Intervals

\frac{- 5 - 1}{2} < x < \frac{- 5 + 1}{2} or \frac{5 - 1}{2} < x < \frac{5 + 1}{2}

∣ 5 x - 10 ∣ > 0

∣ 2 x - 4 ∣ < ∣ x - 1 ∣

\frac{1}{x - 3} > 6

\frac{( 3 + x )}{x} > 2

lo g_{∣ x ∣} (9 - x^{2} - x - 1) \geq 1

What is |x^2-1|<|x| ?
The solution to |x^2-1|<|x| is (-sqrt(5)-1)/2 <x<(-sqrt(5)+1)/2 \lor (sqrt(5)-1)/2 <x<(sqrt(5)+1)/2