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

The solution to |x^2-3x|+x-2>0 is x -sqrt(2)+2

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

x^{2} - 3 x + x - 2 > 0

x < - 3 + 1 or x > - 2 + 2

Interval Notation

(- \infty, - 3 + 1) \cup (- 2 + 2, \infty)

Decimal Notation

x < - 0.73205 \dots or x > 0.58578 \dots

Solution steps

x^{2} - 3 x + x - 2 > 0

Find positive and negative intervals

x \leq 0, 0 < x < 3, x \geq 3

Solve the inequality for each interval

x < - 3 + 1 or - 2 + 2 < x < 3 or x \geq 3

Merge Overlapping Intervals

x < - 3 + 1 or x > - 2 + 2

\frac{( x ^{2} - ∣ x ∣ - 2 )}{( 2 ∣ x ∣ - x ^{2} - 2 )} > 2

∣ 3 d - 3 ∣ > 12

∣ x - 4 ∣ + 2 ∣ x - 3 ∣ \geq 4

∣ 2 x + 7 ∣ < ∣ 5 ∣

(1 + x^{2}) \geq 1 - x^{2}

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