What is -3+x<8 x/3+2<(14)/(3+2x) ?

The solution to -3+x<8 x/3+2<(14)/(3+2x) is -3<x<(-9-sqrt(177))/8 \lor-3/2 <x<(sqrt(177)-9)/8

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-3+x<8 x/3+2<(14)/(3+2x)

- 3 + x < 8 \frac{x}{3} + 2 < \frac{14}{3 + 2 x}

- 3 < x < \frac{- 9 - 177}{8} or - \frac{3}{2} < x < \frac{177 - 9}{8}

Interval Notation

(- 3, \frac{- 9 - 177}{8}) \cup (- \frac{3}{2}, \frac{177 - 9}{8})

Decimal Notation

- 3 < x < - 2.78801 \dots or - 1.5 < x < 0.53801 \dots

Solution steps

- 3 + x < 8 \cdot \frac{x}{3} + 2 < \frac{14}{3 + 2 x}

a < u < b

then

a < u and u < b

- 3 + x < 8 \cdot \frac{x}{3} + 2 and 8 \cdot \frac{x}{3} + 2 < \frac{14}{3 + 2 x}

- 3 + x < 8 \cdot \frac{x}{3} + 2 : x > - 3

8 \cdot \frac{x}{3} + 2 < \frac{14}{3 + 2 x} : x < \frac{- 9 - 177}{8} or - \frac{3}{2} < x < \frac{177 - 9}{8}

Combine the intervals

x > - 3 and (x < \frac{- 9 - 177}{8} or - \frac{3}{2} < x < \frac{177 - 9}{8})

Merge Overlapping Intervals

- 3 < x < \frac{- 9 - 177}{8} or - \frac{3}{2} < x < \frac{177 - 9}{8}

\frac{1}{4} + \frac{5}{12} + \frac{( - 1 )}{13} < x < \frac{17}{5} + \frac{2}{10} + \frac{1}{2}

0 < \frac{6}{x} < \frac{6}{7}

\frac{- 12}{17} < x < \frac{- 8}{17}

- 1 < 3 + 4 x < 23

- 1 < n < 0

What is -3+x<8 x/3+2<(14)/(3+2x) ?
The solution to -3+x<8 x/3+2<(14)/(3+2x) is -3<x<(-9-sqrt(177))/8 \lor-3/2 <x<(sqrt(177)-9)/8