#### Answer

$x\gt-\dfrac{2}{17}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
2(4+2x)\gt2x+3(2-5x)
,$ use the Distributive Property and 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 inequality above is equivalent to
\begin{array}{l}\require{cancel}
2(4+2x)\gt2x+3(2-5x)
\\\\
2(4)+2(2x)\gt2x+3(2)+3(-5x)
\\\\
8+4x\gt2x+6-15x
.\end{array}
Using the properties of inequality to isolate the variable, then
\begin{array}{l}\require{cancel}
8+4x\gt2x+6-15x
\\\\
4x-2x+15x\gt6-8
\\\\
17x\gt-2
\\\\
x\gt-\dfrac{2}{17}
.\end{array}