What is (|x-1|)/(|x-2|)<4 ?

The solution to (|x-1|)/(|x-2|) 7/3

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(|x-1|)/(|x-2|)<4

\frac{∣ x - 1 ∣}{∣ x - 2 ∣} < 4

x < \frac{9}{5} or x > \frac{7}{3}

Interval Notation

(- \infty, \frac{9}{5}) \cup (\frac{7}{3}, \infty)

Decimal Notation

x < 1.8 or x > 2.33333 \dots

Solution steps

\frac{∣ x - 1 ∣}{∣ x - 2 ∣} < 4

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{9}{5} or x > \frac{7}{3}

Merge Overlapping Intervals

x < \frac{9}{5} or x > \frac{7}{3}

\frac{1}{3} \leq (\frac{1}{3})^{x - 1} \leq 9

\frac{1}{2} - \frac{1}{3} x = \frac{4}{3}

\frac{4}{7} \cdot \frac{1}{10}

\frac{38}{72} - \frac{22}{180} - \frac{14}{160}

4 - x = ∣ 2 - 3 x ∣

What is (|x-1|)/(|x-2|)<4 ?
The solution to (|x-1|)/(|x-2|)<4 is x< 9/5 \lor x> 7/3