|2x-3|<x+1

Solution

∣ 2 x - 3 ∣ < x + 1

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

Interval Notation

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

Decimal Notation

0.66666 \dots < x < 4

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

Merge Overlapping Intervals

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

x^{2} - 4 x < 5, ∣ x + 1 ∣ < 3

\frac{( 3 x )}{4 - 2} < 8

∣ 19 + 3 x ∣ \geq 46

\frac{( x - 4 )}{5} < 4

x^{2} - ∣ 3 x + 2 ∣ + x \leq 0