What is x^2-7x+12<|x-4| ?

The solution to x^2-7x+12<|x-4| is 2<x<4

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x^2-7x+12<|x-4|

x^{2} - 7 x + 12 < ∣ x - 4 ∣

2 < x < 4

Solution steps

x^{2} - 7 x + 12 < ∣ x - 4 ∣

Find positive and negative intervals

x < 4, x \geq 4

Solve the inequality for each interval

2 < x < 4 or No Solution

Merge Overlapping Intervals

2 < x < 4

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

\frac{( x ^{2} - 3 x - 1 )}{( x ^{2} + x + 1 )} < 3

∣ x ∣ < \frac{2}{x}

x^{2} - ∣ x ∣ - 2 \geq 0

\frac{1 + 3}{x} > 2