What is |3x-4|<|2x-1| ?

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

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|3x-4|<|2x-1|

∣ 3 x - 4 ∣ < ∣ 2 x - 1 ∣

1 < x < 3

Solution steps

∣ 3 x - 4 ∣ < ∣ 2 x - 1 ∣

Find positive and negative intervals

x < \frac{1}{2}, \frac{1}{2} \leq x < \frac{4}{3}, x \geq \frac{4}{3}

Solve the inequality for each interval

No Solution or 1 < x < \frac{4}{3} or \frac{4}{3} \leq x < 3

Merge Overlapping Intervals

1 < x < 3

∣ - 8 x + 4 ∣ < - 1

∣ 1 - x ∣ \leq 5

∣ 2 x - 3 ∣ < x - 1

∣ 4 x - 3 ∣ < 4

∣ x - 1 ∣ ∣ x - 2 ∣ \geq ∣ x + 2 ∣