Answer
$x\lt\dfrac{11}{18}$
Work Step by Step
Using the Distributive Property and the properties of inequality, the solution to the given inequality, $
\dfrac{3}{4}\left(3x-\dfrac{1}{2}\right)-\dfrac{2}{3}\lt\dfrac{1}{3}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{9x}{4}-\dfrac{3}{8}-\dfrac{2}{3}\lt\dfrac{1}{3}
\\\\
24\left( \dfrac{9x}{4}-\dfrac{3}{8}-\dfrac{2}{3} \right) \lt\left( \dfrac{1}{3} \right)24
\\\\
6(9x)+3(-3)+8(-2)\lt1(8)
\\\\
54x-9-16\lt8
\\\\
54x\lt8+9+16
\\\\
54x\lt33
\\\\
x\lt\dfrac{33}{54}
\\\\
x\lt\dfrac{\cancel{3}\cdot11}{\cancel{3}\cdot18}
\\\\
x\lt\dfrac{11}{18}
.\end{array}
