Answer
$\left\{-4, 7\right\}$
Work Step by Step
RECALL:
$|x|=a \longrightarrow x=a \text{ or } x = -a$
Use the rule above to obtain:
$2x-3 = 11 \text{ or } 2x-3 = -11$
Solve each equation to obtain:
$2x = 11+3 \text{ or } 2x = -11 +3
\\2x = 14 \text{ or } 2x =-8
\\x = \frac{14}{2} \text{ or } x = \frac{-8}{2}
\\x=7 \text{ or } x = -4$
Thus, the solution set is $\left\{-4, 7\right\}$.
