What is 2/(|x-2|)>(|-3|)/(|2x-1|) ?

The solution to 2/(|x-2|)>(|-3|)/(|2x-1|) is x 2

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2/(|x-2|)>(|-3|)/(|2x-1|)

\frac{2}{∣ x - 2 ∣} > \frac{∣ - 3 ∣}{∣ 2 x - 1 ∣}

x < - 4 or \frac{8}{7} < x < 2 or x > 2

Solution steps

\frac{2}{∣ x - 2 ∣} > \frac{∣ - 3 ∣}{∣ 2 x - 1 ∣}

Find positive and negative intervals

x < \frac{1}{2}, \frac{1}{2} \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - 4 or \frac{8}{7} < x < 2 or x > 2

x^{2} - ∣ x + 2 ∣ + x > 0

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

x^{2} - x \leq x + 1

∣ 2 x - 3 ∣ > ∣ x + 4 ∣

∣ - 0.5 x ∣ < 1

What is 2/(|x-2|)>(|-3|)/(|2x-1|) ?
The solution to 2/(|x-2|)>(|-3|)/(|2x-1|) is x<-4\lor 8/7 <x<2\lor x>2