Answer
$x=-1\frac{1}{3}\ or\ x=1\frac{1}{3}$
Work Step by Step
$2|3x|+1=9\longrightarrow$ subtract 1 from each side
$2|3x|+1-1=9-1\longrightarrow$ subtract
$2|3x|=8\longrightarrow$ divide both sides by 2
$2|3x|\div2=8\div2\longrightarrow$ divide
$|3x|=4\longrightarrow$ definition of absolute value
$3x=-4\ or\ 3x=4\longrightarrow$ divide all parts by 3
$3x\div3=-4\div3\ or\ 3x\div3=4\div3\longrightarrow$ divide
$x=-1\frac{1}{3}\ or\ x=1\frac{1}{3}$
