What is x^2-|3x-2|>0 ?

The solution to x^2-|3x-2|>0 is x 2

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x^2-|3x-2|>0

x^{2} - ∣ 3 x - 2 ∣ > 0

x < \frac{- 17 - 3}{2} or \frac{17 - 3}{2} < x < 1 or x > 2

Interval Notation

(- \infty, \frac{- 17 - 3}{2}) \cup (\frac{17 - 3}{2}, 1) \cup (2, \infty)

Decimal Notation

x < - 3.56155 \dots or 0.56155 \dots < x < 1 or x > 2

Solution steps

x^{2} - ∣ 3 x - 2 ∣ > 0

Find positive and negative intervals

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

Solve the inequality for each interval

(x < \frac{- 17 - 3}{2} or \frac{17 - 3}{2} < x < \frac{2}{3}) or (\frac{2}{3} \leq x < 1 or x > 2)

Merge Overlapping Intervals

x < \frac{- 17 - 3}{2} or \frac{17 - 3}{2} < x < 1 or x > 2

∣ 9 - x ∣ < 2 - 3 x

∣ x - 1 ∣ + ∣ x - 2 ∣ > 3

- x^{2} - 9 x - 7 \geq 1

∣ x - 2 ∣ > 2 + x - ∣ 3 - x ∣

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \leq 6

What is x^2-|3x-2|>0 ?
The solution to x^2-|3x-2|>0 is x<(-sqrt(17)-3)/2 \lor (sqrt(17)-3)/2 <x<1\lor x>2