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

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

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

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

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

Solution steps

\frac{∣ x ∣ - 3}{∣ 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

∣ 3 x - 4 ∣ < ∣ 2 x - 1 ∣

∣ - 8 x + 4 ∣ < - 1

∣ 1 - x ∣ \leq 5

∣ 2 x - 3 ∣ < x - 1

∣ 4 x - 3 ∣ < 4

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