# How do you solve 3<x/2 +1<= 7 ?

$x \in \left(4 , 12\right]$.
The given inequality is the combined inequality for $3 < \frac{x}{2} + 1 \mathmr{and} \frac{x}{2} + 1 \le 7$.
So, from the first, $x > 4$ and, from the second, $x \le 12$.
Answer $4 < x \le 12 \mathmr{and} x \in \left(4 , 12\right]$.