Question

Solve the inequality $7\le \frac{3x+11}{2}\le 11$

Answer 1

Simplification
Given : $7\le \frac{3x+11}{2}\le 11$
Multiplying with $2$ on all sides
$\Rightarrow 7\times 2\le \frac{3x+11}{2}\times 2\le 11\times 2$
$\Rightarrow 14\le 3x+11\le 22$
Subtracting $11$ on all sides
$\Rightarrow 14-11\le 3x+11-11\le 22-11$
$\Rightarrow 3\le 3x\le 11$
Dividing by $3$ on all sides
$\Rightarrow \frac{3}{3}\le \frac{3x}{3}\le \frac{11}{3}$
$\Rightarrow 1\le x\le \frac{11}{3}$
Hence, $x\in [1,\frac{11}{3}]$