What is |5x-2|<3x+4 ?

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

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|5x-2|<3x+4

∣ 5 x - 2 ∣ < 3 x + 4

- \frac{1}{4} < x < 3

Solution steps

∣ 5 x - 2 ∣ < 3 x + 4

Find positive and negative intervals

x < \frac{2}{5}, x \geq \frac{2}{5}

Solve the inequality for each interval

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

Merge Overlapping Intervals

- \frac{1}{4} < x < 3

\frac{2 x + 2}{6} > 4

∣ x - 5 ∣ + 2 x - 1 \geq ∣ x + 4 ∣

x^{2} - 4 x + 3 \geq x^{2} - 6 x + 8

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

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