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

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

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

\frac{∣ x + 2 ∣}{∣ 2 x - 3 ∣} < 1

x < \frac{1}{3} or x > 5

Interval Notation

(- \infty, \frac{1}{3}) \cup (5, \infty)

Decimal Notation

x < 0.33333 \dots or x > 5

Solution steps

\frac{∣ x + 2 ∣}{∣ 2 x - 3 ∣} < 1

Find positive and negative intervals

x < - 2, - 2 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

x < - 2 or - 2 \leq x < \frac{1}{3} or x > 5

Merge Overlapping Intervals

x < \frac{1}{3} or x > 5

- x^{2} + 2 x + 8 = 0

3 (x + 2) + 2 (x + 4) = 19

(x + 1)^{2} (x - 3) < 0

\frac{5}{6} - \frac{1}{6}

- 3 z > 18

What is (|x+2|)/(|2x-3|)<1 ?
The solution to (|x+2|)/(|2x-3|)<1 is x< 1/3 \lor x>5