What is |x^2-5x+6|<|x^2-2x| ?

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|x^2-5x+6|<|x^2-2x|

x^{2} - 5 x + 6 < x^{2} - 2 x

\frac{3}{2} < x < 2 or x > 2

Interval Notation

(\frac{3}{2}, 2) \cup (2, \infty)

Decimal Notation

1.5 < x < 2 or x > 2

Solution steps

x^{2} - 5 x + 6 < x^{2} - 2 x

Find positive and negative intervals

x \leq 0, 0 < x \leq 2, 2 < x < 3, x \geq 3

Solve the inequality for each interval

No Solution or \frac{3}{2} < x < 2 or 2 < x < 3 or x \geq 3

Merge Overlapping Intervals

\frac{3}{2} < x < 2 or x > 2

x^{2} - 1 > 0

\frac{( ∣ x ∣ - 3 )}{( ∣ x ∣ - 5 )} < 0

∣ 3 x - 4 ∣ < ∣ 2 x - 1 ∣

∣ - 8 x + 4 ∣ < - 1

∣ 1 - x ∣ \leq 5

What is |x^2-5x+6|<|x^2-2x| ?
The solution to |x^2-5x+6|<|x^2-2x| is 3/2 <x<2\lor x>2