What is |3x-2|<|x+2| ?

The solution to |3x-2|<|x+2| is 0<x<2

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|3x-2|<|x+2|

∣ 3 x - 2 ∣ < ∣ x + 2 ∣

0 < x < 2

Interval Notation

(0, 2)

Solution steps

∣ 3 x - 2 ∣ < ∣ x + 2 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or 0 < x < \frac{2}{3} or \frac{2}{3} \leq x < 2

Merge Overlapping Intervals

0 < x < 2

\frac{1}{3} z^{2} - 4 = - \frac{11}{3}

\frac{a ^{2} - 6 a + 9}{a - 3}

\frac{1}{3} - \frac{1}{7}

- p^{2} - 7 p + 70 = 10

(3 x - 10)^{2} - 6 = 1