1. **State the problem:** Solve the equation $-6x + 1 = 13$ for $x$. 2. **Use the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, adding or subtracting the same number on both sides keeps the equation balanced. 3. **Step-by-step solution:** Start with the equation: $$-6x + 1 = 13$$ Subtract 1 from both sides: $$-6x + \cancel{1} - \cancel{1} = 13 - 1$$ $$-6x = 12$$ Divide both sides by $-6$ to isolate $x$: $$\frac{-6x}{\cancel{-6}} = \frac{12}{\cancel{-6}}$$ $$x = -2$$ 4. **Answer:** The solution is $x = -2$. This completes the solution for the first equation.