What is ((|x|-4))/((|x|-5))<= 0 ?

The solution to ((|x|-4))/((|x|-5))<= 0 is -5<x<=-4\lor 4<= x<5

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((|x|-4))/((|x|-5))<= 0

\frac{( ∣ x ∣ - 4 )}{( ∣ x ∣ - 5 )} \leq 0

- 5 < x \leq - 4 or 4 \leq x < 5

Interval Notation

(- 5, - 4] \cup [4, 5)

Solution steps

\frac{∣ x ∣ - 4}{∣ x ∣ - 5} \leq 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

No Solution or - 5 < x \leq - 4 or 4 \leq x < 5

Merge Overlapping Intervals

- 5 < x \leq - 4 or 4 \leq x < 5

∣ x ∣ - ∣ x - 2 ∣ \geq 1

\frac{3 - x}{2} \leq 2

\frac{( 2 x - 4 )}{- 6} + 2 \leq 10

∣ z - 1 ∣ + ∣ z + 1 ∣ \leq 3

∣ 2 x + 3 ∣ > \frac{1}{2}

What is ((|x|-4))/((|x|-5))<= 0 ?
The solution to ((|x|-4))/((|x|-5))<= 0 is -5<x<=-4\lor 4<= x<5