#### Answer

$x\gt-7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
8-x\lt15
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
8-x\lt15
\\\\
-x\lt15-8
\\\\
-x\lt7
.\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\lt7
\\\\
x\gt\dfrac{7}{-1}
\\\\
x\gt-7
.\end{array}