Answer
$m\le2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4m+7\ge9m-3
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given inequality is equivalent to
\begin{array}{l}\require{cancel}
4m+7\ge9m-3
\\\\
4m-9m\ge-3-7
\\\\
-5m\ge-10
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5m\ge-10
\\\\
m\le\dfrac{-10}{-5}
\\\\
m\le2
.\end{array}
