Variables and Algebraic Expressions

What Is a Variable?

A variable is a letter (like $x$, $y$, or $n$) that represents an unknown number.

Algebraic Expressions

An algebraic expression contains numbers, variables, and operations.

| Expression | Meaning | |-----------|---------| | $x + 5$ | A number plus 5 | | $3x$ | 3 times a number | | $\frac{x}{2}$ | A number divided by 2 | | $x^2 - 4$ | A number squared minus 4 |

Evaluating Expressions

Substitute the value of the variable and calculate.

Evaluate $3x + 7$ when $x = 4$: $3(4) + 7 = 12 + 7 = 19$

Evaluate $x^2 - 2x + 1$ when $x = 3$: $3^2 - 2(3) + 1 = 9 - 6 + 1 = 4$

Combining Like Terms

Like terms have the same variable raised to the same power.

$5x + 3x = 8x \qquad 7y - 2y = 5y$ $4x + 3y + 2x + y = 6x + 4y$

The Distributive Property

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

$3(x + 4) = 3x + 12$ $-2(3x - 5) = -6x + 10$

Remember: When writing expressions, $5 \times x$ is written as $5x$ (skip the multiplication sign).