#### Answer

$x\gt-\dfrac{1}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
3-2(x+3)\lt4x
,$ use first the Distributive Property. Then use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3-2(x)-2(3)\lt4x
\\\\
3-2x-6\lt4x
.\end{array}
Using the properties of inequality to combine like terms, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2x-4x\lt-3+6
\\\\
-6x\lt3
.\end{array}
Dividing both sides by $
-6
,$ in which the inequality symbol reverses, results to
\begin{array}{l}\require{cancel}
x\gt\dfrac{3}{-6}
\\\\
x\gt-\dfrac{1}{2}
.\end{array}