|2x-3|<x-1

Solution

∣ 2 x - 3 ∣ < x - 1

\frac{4}{3} < x < 2

Interval Notation

(\frac{4}{3}, 2)

Decimal Notation

1.33333 \dots < x < 2

Solution steps

∣ 2 x - 3 ∣ < x - 1

Find positive and negative intervals

x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

\frac{4}{3} < x < \frac{3}{2} or \frac{3}{2} \leq x < 2

Merge Overlapping Intervals

\frac{4}{3} < x < 2

∣ 4 x - 3 ∣ < 4

∣ x - 1 ∣ ∣ x - 2 ∣ \geq ∣ x + 2 ∣

∣ 7 y ∣ - 2 > 5

x^{2} + 5 x < 6, ∣ x + 1 ∣ < 2

∣ x - 1 ∣ > - 1