Chapter 3 - Introduction to Graphing - 3.7 Point-Slope Form and Equations of Lines - 3.7 Exercise Set - Page 220: 91

$x\lt-\dfrac{17}{3}$

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}