Variables and Expressions

Variables

A variable is a letter that represents an unknown number.

Common variables: $x, y, n, a, b$

Example: If $x = 5$, then $x + 3 = 5 + 3 = 8$

Algebraic Expression

A combination of variables, numbers, and operations.

Examples:

• $2x + 5$
• $3n - 7$
• $\frac{x}{4} + 2$

Evaluating Expressions

Substitute the value for the variable and calculate.

Example: Evaluate $3x - 4$ when $x = 5$ $3(5) - 4 = 15 - 4 = 11$

Terms

Parts of an expression separated by $+$ or $-$ signs.

Example: In $3x + 2y - 5$

• Three terms: $3x$, $2y$, and $-5$

Coefficients

The number part of a term with a variable.

Example: In $5x$, the coefficient is $5$

Like Terms

Terms with the same variable raised to the same power.

Like terms:

• $3x$ and $7x$
• $2y^2$ and $5y^2$

NOT like terms:

• $3x$ and $3y$ (different variables)
• $x$ and $x^2$ (different powers)

Combining Like Terms

Add or subtract the coefficients, keep the variable part.

$5x + 3x = 8x$ $7y - 2y = 5y$