Answer
$x\lt-\dfrac{17}{3}$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
2(x-7)\gt5x+3
$, is
\begin{array}{l}\require{cancel}
2(x)-2(7)\gt5x+3
\\\\
2x-14\gt5x+3
\\\\
2x-5x\gt3+14
\\\\
-3x\gt17
\\\\
x\lt\dfrac{17}{-3}
\\\\
x\lt-\dfrac{17}{3}
.\end{array}