#### Answer

Interval: $[-54, 42]$

#### Work Step by Step

$2| \frac{1}{2}x+3|+3\leq 51$
$2| \frac{1}{2}x+3|\leq 51-3$
$2|\frac{1}{2}x+3|\leq 48$
$|\frac{1}{2}x+3|\leq 48/2$
$|\frac{1}{2}x+3|\leq 24$
$-24\leq\frac{1}{2}x+3\leq 24$
$-27\leq\frac{1}{2}x\leq 21$
$-54\leq x\leq 42$
Interval: $[-54, 42]$