Answer
$\left( -\infty, -\dfrac{12}{5} \right]$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{7}{12}x-\dfrac{1}{3}\le\dfrac{3}{8}x-\dfrac{5}{6}
$ simplifies to
\begin{array}{l}
24\left( \dfrac{7}{12}x-\dfrac{1}{3} \right)\le\left( \dfrac{3}{8}x-\dfrac{5}{6} \right)24\\\\
2(7x)-8(1)\le3(3x)-4(5)\\
14x-8\le9x-20\\
14x-9x\le-20+8\\
5x\le-12\\
x\le-\dfrac{12}{5}
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -\dfrac{12}{5} \right]
$.