What is ((3-|x|))/((|x|-5))>0 ?

The solution to ((3-|x|))/((|x|-5))>0 is -5<x<-3\lor 3<x<5

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((3-|x|))/((|x|-5))>0

\frac{( 3 - ∣ x ∣ )}{( ∣ x ∣ - 5 )} > 0

- 5 < x < - 3 or 3 < x < 5

Solution steps

\frac{3 - ∣ x ∣}{∣ x ∣ - 5} > 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

No Solution or - 5 < x < - 3 or 3 < x < 5

Merge Overlapping Intervals

- 5 < x < - 3 or 3 < x < 5

- 5 ∣ x - 3 ∣ - 5 < 15

∣ 4 x - 3 ∣ \leq 4 - 3 x

∣ x - 28 ∣ \leq 2

x^{2} - 2 x - 3 > x^{2} + 7 x - 13

\frac{( 2 x ^{2} - 4 )}{3} \geq 2 x^{2}

What is ((3-|x|))/((|x|-5))>0 ?
The solution to ((3-|x|))/((|x|-5))>0 is -5<x<-3\lor 3<x<5