What is ((x^2-|x|-12))/((x-3))>= 2x ?

The solution to ((x^2-|x|-12))/((x-3))>= 2x is x<3

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((x^2-|x|-12))/((x-3))>= 2x

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

x < 3

Solution steps

\frac{x ^{2} - ∣ x ∣ - 12}{x - 3} \geq 2 x

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x < 0 or 0 \leq x < 3 or No Solution

Merge Overlapping Intervals

x < 3

∣ t ∣ < 1

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

∣ 3 x - 4 ∣ > 2 - 5 x

\frac{2}{( x - 4 )} > 1

x^{2} - 6 x + 9 \geq 4

What is ((x^2-|x|-12))/((x-3))>= 2x ?
The solution to ((x^2-|x|-12))/((x-3))>= 2x is x<3