Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 16

$x=\dfrac{7}{6}$

Using the properties of equality, the solution to the given equation, $ 6x-5=2 $, is \begin{array}{l} 6x-5+5=2+5 \\\\ 6x=7 \\\\ \dfrac{6x}{6}=\dfrac{7}{6} \\\\ x=\dfrac{7}{6} .\end{array} Checking: \begin{array}{l} 6\left( \dfrac{7}{6} \right)-5=2 \\\\ 7-5=2 \\\\ 2=2 \text{ (TRUE)} .\end{array} Hence, the solution is $ x=\dfrac{7}{6} $.