Answer
$\{x\ |\ x\lt-7\}\cup\{x\ |\ x\gt21\}$
Work Step by Step
$2|x-7|\gt28\longrightarrow$ divide each side by 2
$2|x-7|\div2\gt28\div2\longrightarrow$ divide
$|x-7|\gt14\longrightarrow$ write a compound inequality using the definition of absolute values
$x-7\lt-14$ OR $x-7\gt14\longrightarrow$ solve each inequality
$x-7\lt-14\longrightarrow$ add 7 to each side
$x-7+7\lt-14+7\longrightarrow$ add
$x\lt-7$
OR
$x-7\gt14\longrightarrow$ add 7 to each side
$x-7+7\gt14+7\longrightarrow$ add
$x\gt21$
A compound inequality joined by OR is the union of the two solution sets.
