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

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

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

\frac{∣ x + 1 ∣}{∣ x - 2 ∣} < 1

x < \frac{1}{2}

Interval Notation

(- \infty, \frac{1}{2})

Decimal Notation

x < 0.5

Solution steps

\frac{∣ x + 1 ∣}{∣ x - 2 ∣} < 1

Find positive and negative intervals

x < - 1, - 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

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

Merge Overlapping Intervals

x < \frac{1}{2}

x^{2} + x - 20 \geq 0

\frac{1 - 0.99}{0.99} \cdot 100

\frac{x ^{2} - x y}{9 y ^{2}} \cdot \frac{3 y}{2 x}

x^{2} - 10 x + 24 \leq 0

\frac{4 p ^{6} q ^{- 2}}{24 p ^{6} q ^{9}}