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

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

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1/((2-|x|))>= 1

\frac{1}{( 2 - ∣ x ∣ )} \geq 1

- 2 < x \leq - 1 or 1 \leq x < 2

Interval Notation

(- 2, - 1] \cup [1, 2)

Solution steps

\frac{1}{2 - ∣ x ∣} \geq 1

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

No Solution or - 2 < x \leq - 1 or 1 \leq x < 2

Merge Overlapping Intervals

- 2 < x \leq - 1 or 1 \leq x < 2

x^{2} - 3 x - 3 > x^{2} + 7 x - 13

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

\frac{( ∣ x ∣ + 4 )}{( ∣ x ∣ + 3 )} \geq 0

∣ x - 1 ∣ < ∣ x ∣

x^{2} + x + ∣ x ∣ + 1 < 0

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