What is log_{x^2}(((4x-5))/(|x-2|))>= 1/2 ?

The solution to log_{x^2}(((4x-5))/(|x-2|))>= 1/2 is -1+sqrt(6)<= x<2\lor 2<x<= 5

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log_{x^2}(((4x-5))/(|x-2|))>= 1/2

lo g_{x^{2}} (\frac{( 4 x - 5 )}{∣ x - 2 ∣}) \geq \frac{1}{2}

- 1 + 6 \leq x < 2 or 2 < x \leq 5

Solution steps

lo g_{x^{2}} (\frac{4 x - 5}{∣ x - 2 ∣}) \geq \frac{1}{2}

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

- 1 + 6 \leq x < 2 or 2 < x \leq 5

∣ 2 x - 2 ∣ \leq 6

∣ 3 x ∣ > 1

∣ 5 - (m - 3) ∣ + 8 < 15

∣ 4 x - 3 ∣ < 10

∣ x ∣ - 2 < 1

What is log_{x^2}(((4x-5))/(|x-2|))>= 1/2 ?
The solution to log_{x^2}(((4x-5))/(|x-2|))>= 1/2 is -1+sqrt(6)<= x<2\lor 2<x<= 5