1. **State the problem:** Simplify the expression $15x + 5x$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same. 3. **Intermediate work:** $$15x + 5x = (15 + 5)x = 20x$$ 4. **Explanation:** Since both terms have the variable $x$, we add the coefficients $15$ and $5$ to get $20$, then multiply by $x$. 5. **Final answer:** $$20x$$