Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 95: 93

$a=2$

Using the properties of equality, the solution to the given equation, $ a+(a-3)=(a+2)-(a+1) $, is \begin{array}{l} a+a-3=a+2-a-1 \\\\ 2a-3=1 \\\\ 2a=1+3 \\\\ 2a=4 \\\\ a=\dfrac{4}{2} \\\\ a=2 .\end{array} CHECKING: \begin{array}{l} 2+(2-3)=(2+2)-(2+1) \\\\ 2+(-1)=(4)-(3) \\\\ 1=1 \text{ (TRUE)} .\end{array} Hence, the solution is $ a=2 $.