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

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

\frac{1}{∣ x ∣ - 3} < \frac{1}{2}

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

Interval Notation

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

Solution steps

\frac{1}{∣ x ∣ - 3} < \frac{1}{2}

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

x^{2} - 1 \leq 4

∣ x - 2 ∣ + ∣ x - 4 ∣ > 6

x^{2} - ∣ 3 x + 2 ∣ + x \geq 0

\frac{x + 5}{∣ 1 - x ∣} > 1

∣ 2 x - 10 ∣ > 10

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