What is 1/(|x-2|)>= 1/4 ?

The solution to 1/(|x-2|)>= 1/4 is -2<= x<2\lor 2<x<= 6

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1/(|x-2|)>= 1/4

\frac{1}{∣ x - 2 ∣} \geq \frac{1}{4}

- 2 \leq x < 2 or 2 < x \leq 6

Interval Notation

[- 2, 2) \cup (2, 6]

Solution steps

\frac{1}{∣ x - 2 ∣} \geq \frac{1}{4}

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

- 2 \leq x < 2 or 2 < x \leq 6

\frac{5}{( 3 - x )} > 1

4 ∣ x - 2 ∣ - 2 - x < 4 x + 1

∣ x - 6 ∣ \geq 4

2 x - 7 x + 12 < ∣ x - 4 ∣

3 ∣ x - 1 ∣ + 2 ∣ x - 2 ∣ + ∣ x - 3 ∣ > 4

What is 1/(|x-2|)>= 1/4 ?
The solution to 1/(|x-2|)>= 1/4 is -2<= x<2\lor 2<x<= 6