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

The solution to 1/((|x|-3)) = 5

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

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

x \leq - 5 or - 3 < x < 3 or x \geq 5

Interval Notation

(- \infty, - 5] \cup (- 3, 3) \cup [5, \infty)

Solution steps

\frac{1}{∣ x ∣ - 3} \leq \frac{1}{2}

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x \leq - 5 or - 3 < x < 0 or 0 \leq x < 3 or x \geq 5

Merge Overlapping Intervals

x \leq - 5 or - 3 < x < 3 or x \geq 5

∣ x ∣^{2} < 9

x^{2} - x < 2

\frac{∣ 2 + x ∣}{∣ 3 - x ∣} \geq 3

∣ x - 3 ∣ > - 1

∣ 6 - w ∣ < 6

What is 1/((|x|-3))<= 1/2 ?
The solution to 1/((|x|-3))<= 1/2 is x<=-5\lor-3<x<3\lor x>= 5