Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 136: 96

$x\ge8$

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $ \dfrac{2}{3}(2x-1)\ge10 ,$ is \begin{array}{l}\require{cancel} 3\cdot\dfrac{2}{3}(2x-1)\ge10\cdot3 \\\\ 2(2x-1)\ge30 \\\\ 2(2x)+2(-1)\ge30 \\\\ 4x-2\ge30 \\\\ 4x\ge30+2 \\\\ 4x\ge32 \\\\ x\ge\dfrac{32}{4} \\\\ x\ge8 .\end{array}