|3x-2|<x+3

Solution

∣ 3 x - 2 ∣ < x + 3

- \frac{1}{4} < x < \frac{5}{2}

Solution steps

∣ 3 x - 2 ∣ < x + 3

Find positive and negative intervals

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

Solve the inequality for each interval

- \frac{1}{4} < x < \frac{2}{3} or \frac{2}{3} \leq x < \frac{5}{2}

Merge Overlapping Intervals

- \frac{1}{4} < x < \frac{5}{2}

∣ x - 3 ∣ > x^{2} - 3

∣ x ∣ + ∣ x - 2 ∣ \leq 6

∣ x - 1 ∣ \leq 1

∣ 3 x ∣ > 5

x^{2} - ∣ x ∣ - 2 > 0