Answer
$\left( -\infty,29 \right]
$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{3}{4}(x-7)\ge x+2
$ simplifies to
\begin{array}{l}
4\cdot\dfrac{3}{4}(x-7)\ge (x+2)\cdot4
\\
3(x-7)\ge 4x+8
\\
3x-21\ge 4x+8
\\
3x-4x\ge 8+21
\\
-x\ge 29
\\
x\le 29
.\end{array}
In interval notation, the solution set is $
\left( -\infty,29 \right]
$.
