Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Mixed Review - Page 373: 56

$c=2$

We start with the given equation: $4c-7=-c+3$ We subtract $4c$ from both sides of the equation: $4c-4c-7=-4c-c+3$ We subtract $3$ from both sides of the equation: $4c-4c-7-3=-4c-c+3-3$ We combine like terms on both sides of the equation: $-10=-5c$ We divide by $-5$ on both sides of the equation: $c=\frac{-10}{-5}=2$