Question: Solve for x:
3x + 8 = 5x + 22
1. **State the problem:** Solve the equation $$3x + 8 = 5x + 22$$ for $$x$$.
2. **Write down the formula and rules:** To solve for $$x$$, we want to isolate $$x$$ on one side of the equation. We can do this by moving all terms involving $$x$$ to one side and constants to the other.
3. **Subtract $$3x$$ from both sides:**
$$3x + 8 - 3x = 5x + 22 - 3x$$
which simplifies to
$$8 = 2x + 22$$
4. **Subtract $$22$$ from both sides:**
$$8 - 22 = 2x + 22 - 22$$
which simplifies to
$$-14 = 2x$$
5. **Divide both sides by $$2$$ to solve for $$x$$:**
$$\frac{-14}{\cancel{2}} = \frac{2x}{\cancel{2}}$$
which simplifies to
$$x = -7$$
6. **Final answer:** $$x = -7$$