Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 42

$x=3$

By combining like terms and by using the properties of equality, the solution to the given equation, $ 6x-5=7+2x $, is \begin{array}{l}\require{cancel} 6x-2x=7+5 \\\\ 4x=12 \\\\ x=\dfrac{12}{4} \\\\ x=3 .\end{array} Checking: \begin{array}{l}\require{cancel} 6(3)-5=7+2(3) \\\\ 18-5=7+6 \\\\ 13=13 \text{ (TRUE)} .\end{array} Hence, $ x=3 $.