1. **State the problem:** Simplify the expression $2x + 32x$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same. 3. **Intermediate work:** $$2x + 32x = (2 + 32)x = 34x$$ 4. **Explanation:** Since both terms have the variable $x$, we add the coefficients $2$ and $32$ to get $34$, then multiply by $x$. 5. **Final answer:** $$34x$$