What is (|x-5|)/(|x+2|)<4 ?

The solution to (|x-5|)/(|x+2|) -3/5

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(|x-5|)/(|x+2|)<4

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

x < - \frac{13}{3} or x > - \frac{3}{5}

Solution steps

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

Find positive and negative intervals

x < - 2, - 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

x < - \frac{13}{3} or - \frac{3}{5} < x < 5 or x \geq 5

Merge Overlapping Intervals

x < - \frac{13}{3} or x > - \frac{3}{5}

x^{2} - 3 x + 2 > 2

x^{2} - 3 x + 2 > 0

∣ 3 x - 2 ∣ > 3 ∣ x - 1 ∣

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 3

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 4

What is (|x-5|)/(|x+2|)<4 ?
The solution to (|x-5|)/(|x+2|)<4 is x<-13/3 \lor x>-3/5