Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 47

$x=4$

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