What is |3x-2|-|x+10|<x ?

The solution to |3x-2|-|x+10|<x is -8/5 <x<12

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|3x-2|-|x+10|<x

∣ 3 x - 2 ∣ - ∣ x + 10 ∣ < x

- \frac{8}{5} < x < 12

Solution steps

∣ 3 x - 2 ∣ - ∣ x + 10 ∣ < x

Find positive and negative intervals

x < - 10, - 10 \leq x < \frac{2}{3}, x \geq \frac{2}{3}

Solve the inequality for each interval

No Solution or - \frac{8}{5} < x < \frac{2}{3} or \frac{2}{3} \leq x < 12

Merge Overlapping Intervals

- \frac{8}{5} < x < 12

u^{- \frac{1}{2}} d u

27 x^{6} + 18 x^{3} y + 3 y^{2}

2 x + 31 < 29

32 \leq 9 w + 5

1 2^{2}