Answer
The solution set is $(-7, +\infty)$.
Refer to the image below for the graph.
Work Step by Step
RECALL:
(1) The Multiplication Property of Inequality states that if a negative number is multiplied to each side of an inequality, the inequality's direction/sense change to its opposite.
Thus, if $a \lt b$ and $c\lt 0$, then $ac \gt bc$.
(2) The addition property of inequalities states that If $a \ge b$, then $a+c \ge b+c$
Use the rule in (1) above by multiplying $-\frac{1}{2}$to both sides of the inequality to obtain:
$\begin{array}{ccc}
&-\frac{1}{2}(-2(x+3)) &\gt &-\frac{1}{2}(8)
\\&x+3 &\gt &-4
\end{array}$
Use the rule in (2) above by adding $-3$ to both sides of the inequality to obtain:
$\begin{array}{ccc}
&x+3 + (-3) &\gt &-4+(-3)
\\&x &\gt &-7
\end{array}$
Thus, the solution set is $(-7, +\infty)$.
