Answer
$\left( -\infty, 2 \right]$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{1}{2}(3x-4)\le\dfrac{3}{4}(x-6)+1
$ simplifies to
\begin{array}{l}
4\left[ \dfrac{1}{2}(3x-4) \right]\le\left[ \dfrac{3}{4}(x-6)+1 \right]4\\\\
2(3x-4)\le3(x-6)+4(1)\\
6x-8\le3x-18+4\\
6x-3x\le-18+4+8\\
3x\le-6\\
x\le-2
.\end{array}
In interval notation, the solution set is $
\left( -\infty, 2 \right]
$.
