Lesson 1 of 4

Variables and Expressions

Build the foundation of algebra: variables as symbols for unknowns; translate verbal phrases to algebraic expressions; evaluate and simplify using like terms and the distributive property.

Core45 min

Variables and Expressions

Introduction

Algebra uses variables (letters) to represent unknown values. This powerful tool allows us to describe patterns, solve problems, and model real-world situations.

Key Concepts

Variables and Constants

Variable: A symbol (usually a letter) that represents an unknown or changing value
Constant: A fixed numerical value
Coefficient: The number multiplying a variable (e.g., in $3x$ , the coefficient is $3$ )
Term: A single number, variable, or product of numbers and variables

Translating Verbal Phrases

Verbal Phrase	Algebraic Expression
"5 more than a number"	$x + 5$
"the product of 3 and y"	$3y$
"twice a number decreased by 7"	$2n - 7$
"the sum of x and 4"	$x + 4$
"the quotient of a and b"	$\frac{a}{b}$

Simplifying Expressions

Combine like terms (terms with the same variable and exponent): $3x + 5x = 8x$ $4y^2 - 2y^2 + y = 2y^2 + y$

The Distributive Property

$a(b + c) = ab + ac$

Example: $3(x + 4) = 3x + 12$

Practice Examples

Work through these step-by-step to master the concepts!

Read: Detailed Article with Examples

10 min · read

Understanding Algebraic Expressions

Breaking Down Expressions

Consider the expression: 5x + 3y - 7

5x: coefficient 5, variable x
3y: coefficient 3, variable y
-7: constant term

Like Terms

Terms with the same variables and exponents can be combined:

3x + 5x = 8x âœ“
4y + 2x â‰ combined (different variables) âœ—

Interactive: Expression Builder

15 min · practice

Use the Desmos calculator to experiment with different expressions and see how changing variables affects the result.

Practice: Check Your Understanding

8 min · quiz

Question

Which expression represents 'seven less than twice a number'?

$7 - 2x$$2x - 7$$x/2 - 7$$2(x - 7)$

Question

Simplify: $3x + 5 + 2x - 1$

$5x + 4$$5x + 6$$10x$$3x + 7$

Question

If $x = 4$ , evaluate the expression $3x + 7$

Next Lesson

Key Concepts

Variables and Constants

Variable: A symbol (usually a letter) that represents an unknown or changing value

Constant: A fixed numerical value

Coefficient: The number multiplying a variable (e.g., in

3x

, the coefficient is

3

)

Term: A single number, variable, or product of numbers and variables

Translating Verbal Phrases

Verbal Phrase	Algebraic Expression
"5 more than a number"	$x + 5$
"the product of 3 and y"	$3y$
"twice a number decreased by 7"	$2n - 7$
"the sum of x and 4"	$x + 4$
"the quotient of a and b"	$\frac{a}{b}$