Chapter 2 - Equations, Inequalities, and Problem Solving - 2.1 Solving Equations - 2.1 Exercise Set - Page 87: 79

$a=-\dfrac{1}{2}$

Using properties of equality, the solution to the given equation, $ a-\dfrac{1}{6}=-\dfrac{2}{3} $, is \begin{array}{l}\require{cancel} a-\dfrac{1}{6}+\dfrac{1}{6}=-\dfrac{2}{3}+\dfrac{1}{6} \\\\ a=-\dfrac{4}{6}+\dfrac{1}{6} \\\\ a=-\dfrac{3}{6} \\\\ a=-\dfrac{\cancel{3}}{\cancel{3}\cdot2} \\\\ a=-\dfrac{1}{2} .\end{array}