What is |x-6|>|x^2-5x+9| ?

The solution to |x-6|>|x^2-5x+9| is 1<x<3

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|x-6|>|x^2-5x+9|

∣ x - 6 ∣ > x^{2} - 5 x + 9

1 < x < 3

Interval Notation

(1, 3)

Solution steps

∣ x - 6 ∣ > x^{2} - 5 x + 9

Find positive and negative intervals

x < 6, x \geq 6

Solve the inequality for each interval

1 < x < 3 or No Solution

Merge Overlapping Intervals

1 < x < 3

\frac{x + 1}{x} < 4

x^{2} - 2 x - 8 > 2 x

3 ∣ 5 - 2 x ∣ > 7

∣ 7 x - 5 ∣ > - 2

x^{2} - 2 < 1