Answer
$\{x\ |\ -3\lt x\}\cap\{x\ |\ x\lt6\frac{1}{3}\}$
Work Step by Step
$|3x-5|\lt14\longrightarrow$ write and solve a compound inequality
$-14\lt3x-5$ AND $3x-5\lt14$
$-14\lt3x-5\longrightarrow$ add 5 to each side
$-14+5\lt3x-5+5\longrightarrow$ add
$-9\lt3x\longrightarrow$ divide each side by 3
$-9\div3\lt3x\longrightarrow$ divide
$-3\lt x$
AND
$3x-5\lt14\longrightarrow$ add 5 to each side
$3x-5+5\lt14+5\longrightarrow$ add
$3x\lt19\longrightarrow$ divide each side by 3
$3x\div3\lt19\div3\longrightarrow$ divide
$x\lt6\frac{1}{3}$
The solution of a compound inequality joined by AND is the intersection of the inequalities.
