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

The solution to |x^2-3x|+x-2<0 is -sqrt(3)+1<x<-sqrt(2)+2

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

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

- 3 + 1 < x < - 2 + 2

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

- 3 + 1 < x \leq 0 or 0 < x < - 2 + 2 or No Solution

Merge Overlapping Intervals

- 3 + 1 < x < - 2 + 2

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

\frac{( x - 3 )}{( x + 1 )} \leq 1

x - 1 - x^{2} \leq x^{2} - 3 x + 4

x^{2} - 5 ∣ x ∣ + 6 < 0

\frac{( 3 x )}{( x ^{2} - 4 )} \leq 1

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