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

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

∣ x - 1 ∣ < x^{2} + 1

x^{3} - x \leq x

\frac{1}{2} - \frac{( 5 x )}{3} \leq 5

\frac{( ∣ x + 2 ∣ + x )}{( x + 1 )} > 1

∣ x + 7 ∣ + ∣ x ∣ \leq \frac{1}{2}