# Expressions and equations

Algebraic expressions and equations are used throughout the study of algebra, as well as other areas of mathematics. There are different types of expressions and equations, and this section of the website is intended to shed some light on the various types.

## Expressions vs. Equations

Expressions and equations are often used together, but they are not the same thing. An equation can involve multiple expressions, but an expression is not an equation. Generally, an expression is a combination of variables and numbers that undergo operations such as addition, subtraction, multiplication, division, and more. Below are some examples of expressions:

- x + 5
- x - 12
- 7 × 4x - x
^{2} - (x
^{2})(x + 4)

Some expressions can be simpified, and they can be evaluated given a value for the variable(s). Equations on the other hand, have a relationship. Often it is a relationship between two expressions separated by some kind of symbol, be it an equals sign (=), inequality symbol (<, >, ≥), or some other symbol. Generally, we solve equations, while we either evaluate or simplify expressions. Below is an example of an algebraic equation that we can solve using arithmetic and the knowledge that both sides of the equation must stay equal.

x - 4 = 12 - 3x

x + 3x = 12 + 4

4x = 16

x = 4

Explore the rest of the pages in this section to learn more about expressions and equations.