|x-1|<|x|

Solution

∣ x - 1 ∣ < ∣ x ∣

x > \frac{1}{2}

Interval Notation

(\frac{1}{2}, \infty)

Decimal Notation

x > 0.5

Solution steps

∣ x - 1 ∣ < ∣ x ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{1}{2} < x < 1 or x \geq 1

Merge Overlapping Intervals

x > \frac{1}{2}

x^{2} + x + ∣ x ∣ + 1 < 0

∣ x + 1 ∣ + ∣ x ∣ > 3

x^{2} + x + ∣ x ∣ + 1 \leq 0

x^{2} - 1 < ∣ 2 x - 1 ∣

2 ∣ x + 1 ∣ > x + 4