Answer
$\left(-13, \infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-5\lt9x+8-8x
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-5\lt9x+8-8x
\\\\
-9x+8x\lt+8+5
\\\\
-x\lt13
.\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}
-x\lt13
\\\\
\dfrac{-x}{-1}\lt\dfrac{13}{-1}
\\\\
x\gt-13
.\end{array}
Hence, the solution set is $
\left(-13, \infty \right)
.$