What is 3<(5x-7)/2 <= 10 ?

The solution to 3<(5x-7)/2 <= 10 is 13/5 <x<= 27/5

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3<(5x-7)/2 <= 10

3 < \frac{5 x - 7}{2} \leq 10

\frac{13}{5} < x \leq \frac{27}{5}

Solution steps

3 < \frac{5 x - 7}{2} \leq 10

a < u \leq b

then

a < u and u \leq b

3 < \frac{5 x - 7}{2} and \frac{5 x - 7}{2} \leq 10

3 < \frac{5 x - 7}{2} : x > \frac{13}{5}

\frac{5 x - 7}{2} \leq 10 : x \leq \frac{27}{5}

Combine the intervals

x > \frac{13}{5} and x \leq \frac{27}{5}

Merge Overlapping Intervals

\frac{13}{5} < x \leq \frac{27}{5}

\frac{2 k ^{3} + 9 k ^{2} + 13 k + 6}{6}

x^{2} - 13 x + 40 < 0

x^{2} + 2 x y - 63 y^{2}

2 k^{2} + 7 k + 5

10 p^{3} - 1960 p