Answer
$\left( -\infty,4 \right]$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
48+x\ge5(2x+4)-2x
,$ is
\begin{array}{l}\require{cancel}
48+x\ge10x+20-2x
\\\\
48+x\ge8x+20
\\\\
x-8x\ge20-48
\\\\
-7x\ge-28
\\\\
x\le\dfrac{-28}{-7}
\\\\
x\le4
.\end{array}
In interval notation, the solution is $
\text{the interval }
\left( -\infty,4 \right]
.$
