What is |2x-4|<|x-1| ?

The solution to |2x-4|<|x-1| is 5/3 <x<3

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|2x-4|<|x-1|

∣ 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 < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or \frac{5}{3} < x < 2 or 2 \leq x < 3

Merge Overlapping Intervals

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

\frac{1}{x - 3} > 6

\frac{( 3 + x )}{x} > 2

lo g_{∣ x ∣} (9 - x^{2} - x - 1) \geq 1

∣ 3 x - 2 ∣ + ∣ x + 4 ∣ > 8

\frac{2}{x - 12} > \frac{6}{5}