Algebra 101 - Unit 1

The Language of Algebra

Before beginning Algebra 101 it is helpful to understand key terms and concepts. It is highly recommended to review the Reference Hub section location on the Math main directory page. In the reference hub will be a link titled "Key Algebra Concepts" that will make learning Algebra faster.

Variables

A variable is a symbol (like 𝑥 , 𝑦 , 𝑛 x,y,n) that stands for a number we don’t yet know, or that can change. Think of it as a placeholder.

Example: The area of a rectangle is written in formula notation as 𝐴 = 𝑙 × 𝑤 . Here, 𝑙 and 𝑤 are variables because they can take different values. They are sometimes written in script to signify they are variables and not something else.

Numerals

A numeral is just a symbol that represents a number.

Expressions

An expression is a combination of numerals, variables, and operations. Examples include \(2+5\) or \(a^2\). The key point is that expressions do not have an equal sign. They are “unfinished thoughts” in algebra.

Statements

A statement is a complete thought in math that can be true or false.

Example: \(5+3=8\) is true while 7<2 is false.

Equations and inequalities are both special kinds of statements.

Equations

An equation is a statement that says two expressions are equal.

Example: 2x+3=7. Equations are solvable, we can find the value of the variable that makes the statement true.

Inequalities

An inequality is a statement that compares two expressions using <,>,≤,≥, and sometimes ≠.

Example: x+4>10. Inequalities don’t just have one solution, they describe ranges of values.

Functions

A function is a special kind of relationship where each input has exactly one output. Often written as 𝑓(𝑥) = f(x)= "some mathematical expression".

Example: f(x)=2x+3. If you plug in x=4, then f(4)=11. Functions are like machines: put a number in, get a number out.

Bringing It Together

1. Numerals are the symbols for numbers.
2. Variables hold the place of missing numbers.
3. Expressions are like an equation but are missing the equal sign and answer.
4. Statements tell us something that’s either true or false.
5. Equations have an equals sign and inequalities have inequality signs.
6. Functions are rules that connect inputs to outputs.