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

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

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

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

3 - 1 < x < 2

Interval Notation

(3 - 1, 2)

Decimal Notation

0.73205 \dots < x < 2

Solution steps

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

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or 3 - 1 < x < 1 or 1 \leq x < 2

Merge Overlapping Intervals

3 - 1 < x < 2

- 2 x + 4 > 10

5 x - 14 \leq 3 x + 8

20 r^{3} + 8 r^{2} + 15 r + 6

- 3 (2 x - 5) = 10 x + 6

6 (\frac{2}{3} x + \frac{1}{3}) + 8 (\frac{1}{4} x - \frac{3}{4}) = 5 x + 4