What is x^2-|5x-3|-x<2 ?

The solution to x^2-|5x-3|-x<2 is -5<x<2sqrt(2)+3

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x^2-|5x-3|-x<2

x^{2} - ∣ 5 x - 3 ∣ - x < 2

- 5 < x < 22 + 3

Solution steps

x^{2} - ∣ 5 x - 3 ∣ - x < 2

Find positive and negative intervals

x < \frac{3}{5}, x \geq \frac{3}{5}

Solve the inequality for each interval

- 5 < x < \frac{3}{5} or \frac{3}{5} \leq x < 22 + 3

Merge Overlapping Intervals

- 5 < x < 22 + 3

\frac{( ∣ x + 4 ∣ + 2 x )}{x + 1} > 2

∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

\frac{3 - ( 5 x - 2 )}{4} \leq 8

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

x^{3} - 1 \geq 1 - x