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

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

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

\frac{- 1}{( ∣ x ∣ - 2 )} \geq 1

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

Solution steps

\frac{- 1}{∣ x ∣ - 2} \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

3 x^{2} - ∣ x - 3 ∣ > 9 x - 2

x^{2} - 2 x - 2 \geq x^{2} - 2

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

∣ t ∣ < 1

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