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

The solution to 2<|(3-x)/(2-3x)|<3 is 1/5 <x< 3/8 \lor 9/10 <x<1

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

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

\frac{1}{5} < x < \frac{3}{8} or \frac{9}{10} < x < 1

Interval Notation

(\frac{1}{5}, \frac{3}{8}) \cup (\frac{9}{10}, 1)

Decimal Notation

0.2 < x < 0.375 or 0.9 < x < 1

Solution steps

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

a < u < b

then

a < u and u < b

2 < \frac{3 - x}{2 - 3 x} and \frac{3 - x}{2 - 3 x} < 3

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

\frac{3 - x}{2 - 3 x} < 3 : x < \frac{3}{8} or x > \frac{9}{10}

Combine the intervals

(\frac{1}{5} < x < \frac{2}{3} or \frac{2}{3} < x < 1) and (x < \frac{3}{8} or x > \frac{9}{10})

Merge Overlapping Intervals

\frac{1}{5} < x < \frac{3}{8} or \frac{9}{10} < x < 1

12 x + 7 < - 11

- \frac{220}{2 ( - 1 )}

\frac{r}{- 2} < - 6

\frac{5 x ^{3} y ^{9}}{20 x ^{2} y ^{- 2}}

- 10 = 10 (k - 9)

What is 2<|(3-x)/(2-3x)|<3 ?
The solution to 2<|(3-x)/(2-3x)|<3 is 1/5 <x< 3/8 \lor 9/10 <x<1