# Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set: 82

$c=1$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $13-(2c+2)=2(c+2)+3c$, is \begin{array}{l} 13-2c-2=2c+4+3c \\\\ 11-2c=5c+4 \\\\ -2c-5c=4-11 \\\\ -7c=-7 \\\\ c=\dfrac{-7}{-7} \\\\ c=1 .\end{array} CHECKING: \begin{array}{l} 13-(2\cdot1+2)=2(1+2)+3\cdot1 \\\\ 13-(4)=2(3)+3 \\\\ 9=6+3 \\\\ 9=9 \text{ (TRUE)} .\end{array} Hence, the solution is $c=1$.

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