1. Let's start by stating the problem: How to add and subtract algebraic expressions. 2. Algebraic expressions are combinations of variables, numbers, and operations like addition and subtraction. When adding or subtracting, we combine like terms. Like terms have the same variable parts raised to the same powers. 3. The general rule for addition and subtraction of algebraic expressions is: $$ (a + b) + (c + d) = a + b + c + d $$ $$ (a + b) - (c + d) = a + b - c - d $$ where $a, b, c, d$ are terms. 4. Example of addition: Add $3x + 5$ and $2x + 7$. Step 1: Write the sum: $$ (3x + 5) + (2x + 7) $$ Step 2: Remove parentheses: $$ 3x + 5 + 2x + 7 $$ Step 3: Group like terms: $$ (3x + 2x) + (5 + 7) $$ Step 4: Add coefficients: $$ 5x + 12 $$ 5. Example of subtraction: Subtract $2x + 7$ from $3x + 5$. Step 1: Write the difference: $$ (3x + 5) - (2x + 7) $$ Step 2: Distribute the minus sign: $$ 3x + 5 - 2x - 7 $$ Step 3: Group like terms: $$ (3x - 2x) + (5 - 7) $$ Step 4: Subtract coefficients: $$ x - 2 $$ 6. Important: Always combine only like terms and be careful with signs when subtracting. This is how you add and subtract algebraic expressions!