1. **State the problem:** Simplify the algebraic expression $3x + 5x - 7$. 2. **Recall the rule:** When simplifying algebraic expressions, combine like terms. Like terms have the same variable raised to the same power. 3. **Identify like terms:** $3x$ and $5x$ are like terms because both have the variable $x$. 4. **Combine like terms:** $$3x + 5x = (3 + 5)x = 8x$$ 5. **Rewrite the expression:** $$8x - 7$$ 6. **Final simplified expression:** $$8x - 7$$ This is the simplest form of the given expression.