What is |((x-2))/((x+4))|<= ((x+3))/((x-6)) ?

The solution to |((x-2))/((x+4))| 6

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|((x-2))/((x+4))|<= ((x+3))/((x-6))

\frac{( x - 2 )}{( x + 4 )} \leq \frac{( x + 3 )}{( x - 6 )}

x > 6

Interval Notation

(6, \infty)

Solution steps

\frac{x - 2}{x + 4} \leq \frac{x + 3}{x - 6}

Find positive and negative intervals

x < - 4, - 4 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or x > 6

Merge Overlapping Intervals

x > 6

∣ x + 3 ∣ + ∣ x - 1 ∣ < ∣ 6 - 3 x ∣

\frac{x ^{2} - 1}{∣ x ^{2} + x + 1 ∣} < 1

x^{2} - 1 \leq 0

∣ 3^{x} - 5 ∣ < 1

x^{2} - 3 ∣ x ∣ - 10 < 0

What is |((x-2))/((x+4))|<= ((x+3))/((x-6)) ?
The solution to |((x-2))/((x+4))|<= ((x+3))/((x-6)) is x>6