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

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

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1<(|x-2|)/(|x+3|)

1 < \frac{∣ x - 2 ∣}{∣ x + 3 ∣}

x < - 3 or - 3 < x < - \frac{1}{2}

Solution steps

1 < \frac{∣ x - 2 ∣}{∣ x + 3 ∣}

Find positive and negative intervals

x < - 3, - 3 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - 3 or - 3 < x < - \frac{1}{2} or No Solution

Merge Overlapping Intervals

x < - 3 or - 3 < x < - \frac{1}{2}

∣ 2 k - 1 ∣ \leq 2

x^{2} - 48 x + 576

4 x^{2} = 72

4 x - 2 = x + 9

What is 1<(|x-2|)/(|x+3|) ?
The solution to 1<(|x-2|)/(|x+3|) is x<-3\lor-3<x<-1/2