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

The solution to -3<= ((3x+2))/((x-1))<1 is -3/2 <x<= 1/6

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

- 3 \leq \frac{( 3 x + 2 )}{( x - 1 )} < 1

- \frac{3}{2} < x \leq \frac{1}{6}

Interval Notation

(- \frac{3}{2}, \frac{1}{6}]

Decimal Notation

- 1.5 < x \leq 0.16666 \dots

Solution steps

- 3 \leq \frac{( 3 x + 2 )}{( x - 1 )} < 1

a \leq u < b

then

a \leq u and u < b

- 3 \leq \frac{( 3 x + 2 )}{( x - 1 )} and \frac{( 3 x + 2 )}{( x - 1 )} < 1

- 3 \leq \frac{3 x + 2}{x - 1} : x \leq \frac{1}{6} or x > 1

\frac{3 x + 2}{x - 1} < 1 : - \frac{3}{2} < x < 1

Combine the intervals

(x \leq \frac{1}{6} or x > 1) and - \frac{3}{2} < x < 1

Merge Overlapping Intervals

- \frac{3}{2} < x \leq \frac{1}{6}

x + 3 < 4 x < 6

3 < x - 1 < 8

x - 2 - x + 2 < x < x - 2 + x + 2

\frac{( 3 x - 1 )}{6} \leq \frac{( 2 x + 1 )}{3} \leq \frac{( x + 2 )}{2}

0 < 2 x - \frac{5}{2} < 7

What is -3<= ((3x+2))/((x-1))<1 ?
The solution to -3<= ((3x+2))/((x-1))<1 is -3/2 <x<= 1/6