Skills Handbook - Solving and Writing Linear Equations - Exercises - Page 894: 6

$z=-4$

We start with the given equation: $-6z+1=13-3z$ We subtract $1$ from both sides of the equation, add $3z$ to both sides of the equation, and combine like terms: $$-6z+3z+1-1=13-1-3z+3z$$$$-3z=12$$ We divide by $-3$ on each side of the equation: $$\frac{-3z}{-3}=\frac{12}{-3}$$$$z=-4$$