Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 49

$x\ge-\dfrac{16}{3}$

Multiplying both sides by the $LCD= 28 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{x-3}{7}-\dfrac{x-2}{4}\le\dfrac{9}{14} ,$ is \begin{array}{l}\require{cancel} 4(x-3)-7(x-2)\le2(9) \\\\ 4x-12-7x+14\le18 \\\\ 4x-7x\le18+12-14 \\\\ -3x\le16 \\\\ x\ge\dfrac{16}{-3} \\\\ x\ge-\dfrac{16}{3} .\end{array}