## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$c=\dfrac{43}{2}$
Using $a(b+c)=ab+ac$ (or the Distributive Property) and combining like terms, the value of the variable that satisfies the given expression, $2+3(4+c)=1-5(6-c) ,$ is \begin{array}{l}\require{cancel} 2+12+3c=1-30+5c \\\\ 3c-5c=1-30-2-12 \\\\ -2c=-43 \\\\ c=\dfrac{-43}{-2} \\\\ c=\dfrac{43}{2} .\end{array}