1. **State the problem:** Solve the equation $5x + 1 = -x + 7$ for $x$. 2. **Write down the equation:** $$5x + 1 = -x + 7$$ 3. **Add $x$ to both sides to collect $x$ terms on one side:** $$5x + x + 1 = 7$$ $$6x + 1 = 7$$ 4. **Subtract 1 from both sides to isolate the term with $x$:** $$6x = 7 - 1$$ $$6x = 6$$ 5. **Divide both sides by 6 to solve for $x$:** $$x = \frac{6}{6} = 1$$ **Final answer:** $$x = 1$$