What is ((x-4))/((x+2))<= |((x-2))/((x-1))| ?

The solution to ((x-4))/((x+2)) 1

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((x-4))/((x+2))<= |((x-2))/((x-1))|

\frac{( x - 4 )}{( x + 2 )} \leq \frac{( x - 2 )}{( x - 1 )}

- 2 < x < 1 or x > 1

Solution steps

\frac{x - 4}{x + 2} \leq \frac{x - 2}{x - 1}

Find positive and negative intervals

x < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or - 2 < x < 1 or 1 < x < 2 or x \geq 2

Merge Overlapping Intervals

- 2 < x < 1 or x > 1

x^{2} + x - 6 < 6

∣ x - 1 ∣ \geq ∣ x - 3 ∣

(1 + x)^{2} \geq 1 - x^{2}

x^{2} - 6 x + 8 \leq 4 - x

x^{3} + 1 < x^{2} - x + 1

What is ((x-4))/((x+2))<= |((x-2))/((x-1))| ?
The solution to ((x-4))/((x+2))<= |((x-2))/((x-1))| is -2<x<1\lor x>1