Algebra 101 - Unit 1

Evaluating Expressions

In algebra, an expression is a combination of numbers, variables, and operations (like addition, subtraction, multiplication, division, and exponents). Evaluating an expression means finding its value by substituting numbers for the variables and simplifying using the order of operations (PEMDAS).

1. Steps to Evaluate Expressions

1. Identify the variable(s) in the expression.
2. Substitute the given value(s) for the variable(s).
3. Follow the order of operations (PEMDAS) to simplify the expression.
4. Write the final simplified number as the answer.

2. Examples

Example 1: Evaluate 3x + 5 when x = 2

1. Substitute x = 2: 3(2) + 5
2. Multiply: 6 + 5
3. Add: 11

Example 2: Evaluate 2y² - 3y + 4 when y = 3

1. Substitute y = 3: 2(3)² - 3(3) + 4
2. Exponents first: 2(9) - 9 + 4
3. Multiplication: 18 - 9 + 4
4. Add and subtract left to right: 18 - 9 = 9, then 9 + 4 = 13

Example 3: Evaluate 5(a + 2) - 3 when a = 4

1. Substitute a = 4: 5(4 + 2) - 3
2. Parentheses first: 5(6) - 3
3. Multiplication: 30 - 3
4. Subtraction: 27

3. Tips for Success

• Always substitute variables carefully and double-check the values.
• Follow the order of operations exactly.
• Simplify step by step; never skip steps.
• Check your work by plugging the value back in if needed.

Evaluating expressions is a critical skill in algebra and will help you solve equations, inequalities, and word problems more effectively.