Question

Solve the inequality: $7 ≤ \frac{(3x+11)}{2} ≤ 11$

Answer 1

$7 ≤ \frac{(3x+11)}{2} ≤ 11$
⇒ 14 ≤ 3x+11 ≤ 22
⇒ 14-11 ≤ 3x ≤ 22-11
⇒ 3 ≤ 3x ≤ 11
$⇒ 1 ≤ x ≤ \frac{11}{3}$
Thus, the solution set for the given inequality is $[1, \frac{11}{3}]$.