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

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

∣ x - 1 ∣ < ∣ 2 x - 1 ∣

x < 0 or x > \frac{2}{3}

Interval Notation

(- \infty, 0) \cup (\frac{2}{3}, \infty)

Decimal Notation

x < 0 or x > 0.66666 \dots

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 < 0 or \frac{2}{3} < x < 1 or x \geq 1

Merge Overlapping Intervals

x < 0 or x > \frac{2}{3}

45 + 125 - 5

2 x^{2} + 7 x

a^{2} + 6^{2} = 8^{2}

(0.01)^{2}

- 1 x = x^{2} - 1 + 2