Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 50

$x\ge30$

Multiplying both sides by the $LCD= 30 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{x-1}{5}-\dfrac{x+2}{6}\ge\dfrac{7}{15} ,$ is \begin{array}{l}\require{cancel} 6(x-1)-5(x+2)\ge2(7) \\\\ 6x-6-5x-10\ge14 \\\\ 6x-5x\ge14+6+10 \\\\ x\ge30 .\end{array}