Introduction to Algebra

Algebra is a key part of GCSE Maths and forms the foundation for topics such as equations, graphs, functions, and formulas. This introduction to algebra explains how letters are used to represent numbers and how to solve simple equations step by step.

What is algebra?

Algebra is a branch of maths that uses letters (usually $x$ , $y$ , $a$ , $b$ , etc.) to represent numbers that may be unknown or can change.

Instead of working only with numbers, algebra lets us describe patterns, rules, and relationships.

For example:
$x + 3 = 7$

Here, $x$ represents a number we don’t yet know.

Algebra is used to solve problems, describe situations, and build formulas across many areas of maths.

Example Question:

We will work through a simple algebra problem:

Find the value of $x$ :

$x + 5 = 9$

Exam Tip

When solving algebra problems:

Think of letters as numbers you haven’t found yet
Use inverse operations to isolate the variable
Keep the equation balanced by doing the same to both sides

Method – Solving a Basic Algebra Equation

We want to find the value of the unknown.

Step 1: Identify the operation

In $x + 5 = 9$ , the number $5$ is being added to $x$ .

Step 2: Use the inverse operation

The inverse of $+5$ is $−5$ .

Subtract $5$ from both sides.

Step 3: Solve

$x + 5 − 5 = 9 − 5$

$x = 4$

Worked Example

Solve:

$x − 3 = 8$

Step 1: Identify the operation

$3$ is being subtracted from $x$ .

Step 2: Use the inverse operation

Add $3$ to both sides.

$x − 3 + 3 = 8 + 3$

$x = 11$

Final answer:

$x = 11$

Check your solution (important habit)

Substitute $x = 11$ back into the original equation:

$11 − 3 = 8$ ✔️

The solution is correct.

Think Like a Mathematician

Algebra isn’t just about solving equations — it’s about understanding relationships.

The letter can represent:

An unknown value
A number that can change
A general rule

For example:

Perimeter of a square = $4s$

Here, $s$ represents the length of one side.

Common mistakes to avoid

Treating letters as objects instead of numbers
Forgetting to apply operations to both sides
Mixing up inverse operations
Not checking the solution

Most algebra errors happen because the equation becomes unbalanced.

Try one yourself

Solve the equation:

$x + 7 = 12$

First: Use the inverse operation

Then: Solve for $x$

Frequently Asked Questions

What does the letter actually mean?

A letter represents a number.

Sometimes it’s unknown (like in equations), and sometimes it can vary (like in formulas).

Next Lesson

Continue → Simplifying Algebraic Expressions