Algebra Variables Cheat Sheet

Variable Definition

A variable is a symbol (usually a letter) that represents an unknown number or a quantity that can change.

Example: In the expression 'x + 5', 'x' is the variable.

Constants

A constant is a value that does not change.

Example: In the expression '3x + 7', '3' and '7' are constants.

Coefficients

A coefficient is a number multiplied by a variable.

Example: In the expression '4y - 2', '4' is the coefficient of 'y'.

Expressions

A mathematical phrase that combines numbers, variables, and operations.

Example: 2a + 3b - 5 is an algebraic expression.

Isolating the Variable

The goal is to get the variable alone on one side of the equation.

Example: To solve x + 3 = 7, subtract 3 from both sides to get x = 4.

Addition/Subtraction Property

You can add or subtract the same number from both sides of an equation without changing the solution.

Example: If y - 5 = 2, then y - 5 + 5 = 2 + 5, so y = 7.

Multiplication/Division Property

You can multiply or divide both sides of an equation by the same non-zero number without changing the solution.

Example: If 2z = 10, then 2z / 2 = 10 / 2, so z = 5.

Inverse Operations

Use the opposite operation to isolate the variable (addition/subtraction, multiplication/division).

Example: To solve for 'w' in w/4 = 8, multiply both sides by 4: w = 32

Like Terms

Terms that have the same variable raised to the same power.

Example: 3x and 5x are like terms, but 3x and 5x² are not.

Combining Like Terms Rule

Add or subtract the coefficients of like terms to simplify expressions.

Example: 2y + 5y - y = (2 + 5 - 1)y = 6y

Distributive Property

a(b + c) = ab + ac. Multiply the term outside the parentheses by each term inside.

Example: 3(x + 2) = 3x + 6