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

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

∣ x - 1 ∣ < ∣ 2 x + 1 ∣

x < - 2 or x > 0

Interval Notation

(- \infty, - 2) \cup (0, \infty)

Solution steps

∣ x - 1 ∣ < ∣ 2 x + 1 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 2 or 0 < x < 1 or x \geq 1

Merge Overlapping Intervals

x < - 2 or x > 0

121 x^{2} - 144 y^{2}

(y - 3)^{2} - 64

- x^{2} - 2 x - 1

- 2 x > - 8 and - 3 x < 12

6 z^{2} - z - 15