What is 1/6 <(2x-19)/(12)<= 2/3 ?

The solution to 1/6 <(2x-19)/(12)<= 2/3 is 21/2 <x<= 27/2

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1/6 <(2x-19)/(12)<= 2/3

\frac{1}{6} < \frac{2 x - 19}{12} \leq \frac{2}{3}

\frac{21}{2} < x \leq \frac{27}{2}

Solution steps

\frac{1}{6} < \frac{2 x - 19}{12} \leq \frac{2}{3}

a < u \leq b

then

a < u and u \leq b

\frac{1}{6} < \frac{2 x - 19}{12} and \frac{2 x - 19}{12} \leq \frac{2}{3}

\frac{1}{6} < \frac{2 x - 19}{12} : x > \frac{21}{2}

\frac{2 x - 19}{12} \leq \frac{2}{3} : x \leq \frac{27}{2}

Combine the intervals

x > \frac{21}{2} and x \leq \frac{27}{2}

Merge Overlapping Intervals

\frac{21}{2} < x \leq \frac{27}{2}

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What is 1/6 <(2x-19)/(12)<= 2/3 ?
The solution to 1/6 <(2x-19)/(12)<= 2/3 is 21/2 <x<= 27/2