Evaluate: (20)/(6) < (x+7)/(3) < (31)/(6)

Expression: $\frac{ 20 }{ 6 } < \frac{ x+7 }{ 3 } < \frac{ 31 }{ 6 }$

Separate the compound inequality into two inequalities

$\begin{array} { l }\frac{ x+7 }{ 3 } > \frac{ 20 }{ 6 },\\\frac{ x+7 }{ 3 } < \frac{ 31 }{ 6 }\end{array}$

Solve the inequality for $x$

$\begin{array} { l }x > 3,\\\frac{ x+7 }{ 3 } < \frac{ 31 }{ 6 }\end{array}$

Solve the inequality for $x$

$\begin{array} { l }x > 3,\\x < \frac{ 17 }{ 2 }\end{array}$

Find the intersection

$\begin{align*}&x \in \langle3, \frac{ 17 }{ 2 }\rangle\end{align*}$