#### Answer

$\left( -\infty,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
3(2x-4)-4x\lt2x+3
,$ 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(2x)+3(-4)-4x\lt2x+3
\\\\
6x-12-4x\lt2x+3
\\\\
6x-4x-2x\lt3+12
\\\\
0\lt15
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then the solution set is the set of all real numbers. In interval notation, the solution set is $
\left( -\infty,\infty \right)
.$
The graph of the solution set is the number line itself.