Algebra 1: Variables & Expressions

Learning Objectives

Understand what variables and expressions are
Evaluate expressions with given values
Simplify basic algebraic expressions
Use proper mathematical notation
Apply order of operations (PEMDAS/BODMAS)

1. Understanding Variables

What is a Variable?

A variable is a symbol (usually a letter) that represents an unknown or changing value. In algebra, we use variables to represent numbers we don't know yet or that can change.

Examples of Variables:

x - could represent any number
y - another common variable
n - often used for counting numbers
a, b, c - commonly used in formulas

Try It: Variable Values

See how changing the value of x affects the expression: 2x + 3

x = 5

Result: 13

2. Algebraic Expressions

What is an Expression?

An expression is a combination of numbers, variables, and mathematical operations that represents a value.

Examples:

$3x + 5$
$2a - b$
$x^2 + 2x + 1$
$\frac{a + b}{2}$

3. Evaluating Expressions

How to Evaluate

To evaluate an expression means to find its value when we know the values of the variables.

Example: Evaluate $3x + 2$ when $x = 4$

Step 1: Replace x with 4: $3(4) + 2$

Step 2: Multiply: $12 + 2$

Step 3: Add: $14$

Practice: Evaluate Expressions

Evaluate the expression 2x + 3y for the given values:

x = y =

4. Order of Operations (PEMDAS/BODMAS)

PEMDAS Rule

When evaluating expressions, follow this order:

P Parentheses (Brackets)

E Exponents (Powers)

M Multiplication

D Division

A Addition

S Subtraction

PEMDAS Practice

Simplify the expression: 2 + 3 × 4

5. Interactive Exercises

Exercise 1: Variable Substitution

If $x = 5$ and $y = 3$, what is the value of $2x + y$?

Exercise 2: Expression Evaluation

Evaluate $3a - 2b + 1$ when $a = 4$ and $b = 2$:

Exercise 3: PEMDAS Challenge

Simplify: $2 + 3 \times 4 - 1$