What is 3x^2-|x-3|>9x-2 ?

The solution to 3x^2-|x-3|>9x-2 is x (sqrt(19)+4)/3

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3x^2-|x-3|>9x-2

3 x^{2} - ∣ x - 3 ∣ > 9 x - 2

x < \frac{- 19 + 4}{3} or x > \frac{19 + 4}{3}

Solution steps

3 x^{2} - ∣ x - 3 ∣ > 9 x - 2

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

(x < \frac{- 19 + 4}{3} or \frac{19 + 4}{3} < x < 3) or x \geq 3

Merge Overlapping Intervals

x < \frac{- 19 + 4}{3} or x > \frac{19 + 4}{3}

x^{2} - 2 x - 2 \geq x^{2} - 2

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

∣ t ∣ < 1

\frac{x}{( x ^{2} - x - 1 )} \leq 2

What is 3x^2-|x-3|>9x-2 ?
The solution to 3x^2-|x-3|>9x-2 is x<(-sqrt(19)+4)/3 \lor x>(sqrt(19)+4)/3