What is ((2-|x|))/(|2+x|)<= 3/((|x|-1)) ?

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

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((2-|x|))/(|2+x|)<= 3/((|x|-1))

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

x < - 2 or - 2 < x < - 1 or x > 1

Interval Notation

(- \infty, - 2) \cup (- 2, - 1) \cup (1, \infty)

Solution steps

\frac{2 - ∣ x ∣}{∣ 2 + x ∣} \leq \frac{3}{∣ x ∣ - 1}

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - 2 or - 2 < x < - 1 or No Solution or x > 1

Merge Overlapping Intervals

x < - 2 or - 2 < x < - 1 or x > 1

x^{2} - 3 x + 2 + 2 x - 1 < 0

∣ 3 x + 3 ∣ \leq 2 x + 2

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

4 ∣ x - 3 ∣ - 6 < 10

∣ 2 x - 5 ∣ - 3 ∣ x - 5 ∣ + ∣ 4 - x ∣ \geq 3 x + 5

What is ((2-|x|))/(|2+x|)<= 3/((|x|-1)) ?
The solution to ((2-|x|))/(|2+x|)<= 3/((|x|-1)) is x<-2\lor-2<x<-1\lor x>1