|2x-4|<x-1

Solution

∣ 2 x - 4 ∣ < x - 1

\frac{5}{3} < x < 3

Interval Notation

(\frac{5}{3}, 3)

Decimal Notation

1.66666 \dots < x < 3

Solution steps

∣ 2 x - 4 ∣ < x - 1

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

\frac{5}{3} < x < 2 or 2 \leq x < 3

Merge Overlapping Intervals

\frac{5}{3} < x < 3

x^{2} - x - 2 > 2

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

∣ x ∣ + ∣ x - 4 ∣ > 4

(b) ∣ x + 2 ∣ + 2 \geq 0

\frac{( 3 x + 6 )}{9} \geq 5