Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 503: 74

$x\ge\dfrac{11}{4}$

Multiplying both sides by the $LCD= 6 $ and using the properties of inequality, the solution to the given expression, $ \dfrac{2x}{3}+\dfrac{1}{6}\ge2 ,$ is \begin{array}{l}\require{cancel} 2(2x)+1(1)\ge6(2) \\\\ 4x+1\ge12 \\\\ 4x\ge12-1 \\\\ 4x\ge11 \\\\ x\ge\dfrac{11}{4} .\end{array}