Answer
$y\le-\dfrac{3}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3-8y\ge9-4y
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
3-8y\ge9-4y
\\\\
-8y+4y\ge9-3
\\\\
-4y\ge6
.\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}
-4y\ge6
\\\\
y\le\dfrac{6}{-4}
\\\\
y\le-\dfrac{3}{2}
.\end{array}
