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

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

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1/(|x-2|)>2

\frac{1}{∣ x - 2 ∣} > 2

\frac{3}{2} < x < 2 or 2 < x < \frac{5}{2}

Solution steps

\frac{1}{∣ x - 2 ∣} > 2

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

\frac{3}{2} < x < 2 or 2 < x < \frac{5}{2}

\frac{3 x}{x ^{2} - 4} \leq 1

∣ 2 x - 5 ∣ \geq ∣ x + 2 ∣

∣ x ∣ \leq ∣ x + 1 ∣

\frac{( x ^{2} - ∣ x ∣ - 5 )}{( ∣ x ∣ - 7 )} \geq 2 x

∣ 3 x - 2 ∣ < x + 3