Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Mixed Review - Page 373: 55

$x=-3$

We start with the given equation: $5x+1=3x-5$ We subtract $3x$ from both sides of the equation: $5x-3x+1=3x-3x-5$ We subtract $1$ from both sides of the equation: $5x-3x+1-1=3x-3x-5-1$ We combine like terms on both sides of the equation: $2x=-6$ We divide by $2$ on both sides of the equation: $x=\frac{-6}{2}=-3$