Answer
$\left(-\infty,2 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
7-8y\gt5-7y
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
7-8y\gt5-7y
\\\\
-8y+7y\gt5-7
\\\\
-y\gt-2
.\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}
-y\gt-2
\\\\
\dfrac{-y}{-1}\gt\dfrac{-2}{-1}
\\\\
y\lt2
.\end{array}
Hence, the solution set is $
\left(-\infty,2 \right)
.$
