What is |3x+2|>|2x-1| ?

The solution to |3x+2|>|2x-1| is x -1/5

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|3x+2|>|2x-1|

∣ 3 x + 2 ∣ > ∣ 2 x - 1 ∣

x < - 3 or x > - \frac{1}{5}

Solution steps

∣ 3 x + 2 ∣ > ∣ 2 x - 1 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 3 or - \frac{1}{5} < x < \frac{1}{2} or x \geq \frac{1}{2}

Merge Overlapping Intervals

x < - 3 or x > - \frac{1}{5}

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

x^{2} - 3 x + x - 2 > 0

\frac{( x ^{2} - ∣ x ∣ - 2 )}{( 2 ∣ x ∣ - x ^{2} - 2 )} > 2

∣ 3 d - 3 ∣ > 12

∣ x - 4 ∣ + 2 ∣ x - 3 ∣ \geq 4