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

The solution to |x^2-1|<|2x-1| is -sqrt(3)-1<x<0\lor sqrt(3)-1<x<2

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

x^{2} - 1 < ∣ 2 x - 1 ∣

- 3 - 1 < x < 0 or 3 - 1 < x < 2

Interval Notation

(- 3 - 1, 0) \cup (3 - 1, 2)

Decimal Notation

- 2.73205 \dots < x < 0 or 0.73205 \dots < x < 2

Solution steps

x^{2} - 1 < ∣ 2 x - 1 ∣

Find positive and negative intervals

x \leq - 1, - 1 < x < \frac{1}{2}, \frac{1}{2} \leq x < 1, x \geq 1

Solve the inequality for each interval

- 3 - 1 < x \leq - 1 or - 1 < x < 0 or 3 - 1 < x < 1 or 1 \leq x < 2

Merge Overlapping Intervals

- 3 - 1 < x < 0 or 3 - 1 < x < 2

2 ∣ x + 1 ∣ > x + 4

∣ (x - 1) (x - 5) ∣ > 4

∣ x - 6 ∣ > x^{2} - 5 x + 9

\frac{x + 1}{x} < 4

x^{2} - 2 x - 8 > 2 x

What is |x^2-1|<|2x-1| ?
The solution to |x^2-1|<|2x-1| is -sqrt(3)-1<x<0\lor sqrt(3)-1<x<2