Evaluating Expressions

Evaluating means finding the value of an expression when you know what the variables equal.

Steps to Evaluate

1. Write the expression
2. Substitute the given values
3. Simplify using order of operations (PEMDAS)

Examples

Example 1: Simple Substitution

Evaluate $3x + 2$ when $x = 5$

$3(5) + 2 = 15 + 2 = 17$

Example 2: Multiple Variables

Evaluate $2a + 3b$ when $a = 4$ and $b = 2$

$2(4) + 3(2) = 8 + 6 = 14$

Example 3: With Exponents

Evaluate $x^2 + 2x - 1$ when $x = 3$

$3^2 + 2(3) - 1 = 9 + 6 - 1 = 14$

Order of Operations Reminder

PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Example 4: Using PEMDAS

Evaluate $2(x + 3)^2 - 5$ when $x = 2$

1. Parentheses: $x + 3 = 2 + 3 = 5$
2. Exponents: $5^2 = 25$
3. Multiplication: $2(25) = 50$
4. Subtraction: $50 - 5 = 45$

Common Mistakes

❌ $2x$ when $x = 3$: "23" (wrong - this isn't how multiplication works) ✅ $2x$ when $x = 3$: $2 \times 3 = 6$