What is 4/(|x|-1)<= |x|-1 ?

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4/(|x|-1)<= |x|-1

\frac{4}{∣ x ∣ - 1} \leq ∣ x ∣ - 1

x \leq - 3 or - 1 < x < 1 or x \geq 3

Interval Notation

(- \infty, - 3] \cup (- 1, 1) \cup [3, \infty)

Solution steps

\frac{4}{∣ x ∣ - 1} \leq ∣ x ∣ - 1

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x \leq - 3 or - 1 < x < 0 or 0 \leq x < 1 or x \geq 3

Merge Overlapping Intervals

x \leq - 3 or - 1 < x < 1 or x \geq 3

(3 x - 4)^{2} = 18

a^{3} - 1

n - 14 = 11

∣ 4 y - 1 ∣ \geq 10

What is 4/(|x|-1)<= |x|-1 ?
The solution to 4/(|x|-1)<= |x|-1 is x<=-3\lor-1<x<1\lor x>= 3