Answer
$\left( -\infty, 4 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-3(x-6)\gt2x-2
,$ use the Distributive Property and the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-3(x)-3(-6)\gt2x-2
\\\\
-3x+18\gt2x-2
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-3x-2x\gt-2-18
\\\\
-5x\gt-20
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\lt\dfrac{-20}{-5}
\\\\
x\lt4
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty, 4 \right)
.$
