Answer
The solution set is $(-\infty, 5)$.
Refer to the image below for the graph.
Work Step by Step
RECALL:
(1) The Multiplication Property of Inequality states that if a positive number is multiplied to each side of an inequality, the inequality's direction/sense does not change.
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 $a+c \ge b+c$
On the left side of the inequality, distribute $-3$ to each term of the binomial to obtain:
$\begin{array}{ccc}
&-3(1)-(-3(x) &\lt &12
\\&-3+3x &\lt &12
\end{array}$
Use the rule in (2) above by adding $3$ to both sides of the inequality to obtain:
$\begin{array}{ccc}
&-3+3x+3 &\lt &12+3
\\&3x &\lt &15
\end{array}$
Use the rule in (1) above by multiplying $\frac{1}{3}$ to both sides of the inequality to obtain:
$\begin{array}{ccc}
&\frac{1}{3}(3x) &\lt &\frac{1}{3}(15)
\\&x &\lt &5
\end{array}$
Thus, the solution set is $(-\infty, 5)$.
