What is (-x)/3 < x/2-1/13 < 1/6 ?

The solution to (-x)/3 < x/2-1/13 < 1/6 is 6/65 <x< 19/39

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(-x)/3 < x/2-1/13 < 1/6

\frac{- x}{3} < \frac{x}{2} - \frac{1}{13} < \frac{1}{6}

\frac{6}{65} < x < \frac{19}{39}

Interval Notation

(\frac{6}{65}, \frac{19}{39})

Decimal Notation

0.09230 \dots < x < 0.48717 \dots

Solution steps

\frac{- x}{3} < \frac{x}{2} - \frac{1}{13} < \frac{1}{6}

a < u < b

then

a < u and u < b

\frac{- x}{3} < \frac{x}{2} - \frac{1}{13} and \frac{x}{2} - \frac{1}{13} < \frac{1}{6}

\frac{- x}{3} < \frac{x}{2} - \frac{1}{13} : x > \frac{6}{65}

\frac{x}{2} - \frac{1}{13} < \frac{1}{6} : x < \frac{19}{39}

Combine the intervals

x > \frac{6}{65} and x < \frac{19}{39}

Merge Overlapping Intervals

\frac{6}{65} < x < \frac{19}{39}

\frac{1}{9} < \frac{1}{( 2 x - 1 )} \leq 1

22 < 2 x + 6 < 30

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

0 < \frac{3}{x} < \frac{5}{8}

- 2 \leq \frac{1}{2} - 3 x + \frac{1}{4} \leq \frac{35}{8}

What is (-x)/3 < x/2-1/13 < 1/6 ?
The solution to (-x)/3 < x/2-1/13 < 1/6 is 6/65 <x< 19/39