Find the value of x that satisfies the inequality.|\frac{3x+1}{2}|<1

Find the value of x that satisfies the inequality.
$|\frac{3x+1}{2}|<1$

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Tuthornt

$|\frac{3x+1}{2}|<1$
set up compound inequality by removing the absolute value
$-1<\frac{3x+1}{2}<1$
muttilpying by 2 throughout the inequality
$-2<3x+1<2$
subtracting by 1 throughout the inequality
$-3<3x<1$
Dividing by 3 thriughout the inequality
$-1
$\therefore x\in \left(-1,\frac{1}{3}\right)$