Algebra for beginners
Last reviewed: 14 July 2026
← All articles·Study guide·7 min read
Algebra is where a lot of parents last remember maths going fuzzy. It is far friendlier than it looks. This guide keeps it plain, so you and your child can work through the first ideas together, even if it has been years since you last saw an x.
A letter is just a number in disguise
When we write x, we mean a number we do not know yet. That is all. So x plus 3 means "some number, plus three". If we find out x is 5, then x plus 3 is 8. The letter is a placeholder, nothing more.
Words you will meet
| Word | What it means |
|---|---|
| Term | A single part, like 3x or 5 or y. |
| Coefficient | The number in front of a letter. In 3x, the coefficient is 3. |
| Expression | Terms joined by plus or minus, like 3x plus 2. |
| Equation | Two expressions with an equals sign, like 3x plus 2 = 11. |
Step 1: 3x means three lots of x
Writing a number next to a letter means multiply. So 3x means 3 times x, or three lots of x. If x is 4, then 3x is 12. There is no need for a times sign, the number and letter just sit together.
Step 2: collect like terms
Like terms use the same letter, so you can add them up. Think of x as a fruit. Two apples plus three apples is five apples, so 2x plus 3x is 5x. But you cannot add apples to oranges, so 2x plus 3y has to stay as it is.
- 2x plus 3x = 5x
- 4a plus a = 5a, because a on its own means 1a
- 5x plus 2 plus x = 6x plus 2, adding the x terms and leaving the 2
- 2x plus 3y cannot be combined, because they are different letters
Step 3: keep the equation balanced
An equation is like a set of scales. Both sides are equal, so whatever you do to one side you must do to the other, and it stays balanced. To solve it, get the letter on its own.
- Solve x plus 4 = 10. Take 4 from both sides, so x = 6.
- Solve 3x = 12. Divide both sides by 3, so x = 4.
- Solve 2x plus 1 = 9. Take 1 from both sides to get 2x = 8, then divide by 2, so x = 4.
Check it works
The lovely thing about equations is that you can check your answer. Put it back in and see if both sides match. For 2x plus 1 = 9 we found x = 4. Check: 2 times 4 is 8, plus 1 is 9. It matches, so it is right.
Practise together
Work these out, then check the answers below.
- If x = 5, what is x plus 7?
- If x = 3, what is 4x?
- Simplify 3x plus 2x.
- Simplify 5a plus 2 plus 2a.
- Solve x plus 6 = 15.
- Solve 2x = 14.
- Solve 3x plus 2 = 17.
Four golden rules
- A letter is just a number you do not know yet.
- A number next to a letter means multiply, so 3x is three lots of x.
- You can only add or subtract like terms, the ones with the same letter.
- Keep an equation balanced by doing the same thing to both sides.
Frequently asked questions
When do children start algebra?
The ideas begin in primary with missing-number boxes, and formal algebra with letters starts in Key Stage 3 (Years 7 to 9). It runs right through GCSE, so a calm, confident start really pays off.
I have forgotten all my algebra. Can I still help?
Yes. The first ideas are simple once the jargon is stripped away, and this guide is written so you can learn alongside your child. Working it out together, and being honest when you are both puzzled, is good modelling.
Why do we use letters in maths at all?
Letters let us describe a rule that works for any number, and solve problems where something is unknown. Once a child sees a letter as just a placeholder for a number, the fear usually fades.
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