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Algebra — It's Just Missing Numbers

Algebra explained from scratch. Letters are just mystery numbers. Learn to solve equations, collect like terms, expand brackets and substitute values.

Algebra looks scary because of all the letters. But here's the secret:letters are just mystery numbers you haven't found yet.

If someone says "what + 3 = 7?", you instantly know the answer is 4. That's algebra. We just write it as x + 3 = 7.

Solving Simple Equations

Think of an equation like a set of balance scales. Whatever you do to one side, you must do to the other to keep it balanced.

Worked Example 1 — Solve x + 5 = 12

  1. We want x on its own
  2. Subtract 5 from both sides: x + 5 − 5 = 12 − 5
  3. x = 7

Worked Example 2 — Solve 3x − 4 = 11

  1. Add 4 to both sides: 3x = 15
  2. Divide both sides by 3: x = 15 ÷ 3
  3. x = 5

Check: 3 × 5 − 4 = 15 − 4 = 11 ✓

Collecting Like Terms

Like terms are terms with the same letter (and power). You can add or subtract them.

Example: 3x + 5x = 8x (like saying 3 apples + 5 apples = 8 apples).

But 3x + 5y cannot be simplified — they're different letters (apples and oranges).

Example: Simplify 4x + 3y − 2x + 7y = 2x + 10y.

Expanding Brackets

Multiply everything inside the bracket by the number (or term) outside.

a(b + c) = ab + ac

Worked Example 3 — Expand 3(2x + 5)

  1. 3 × 2x = 6x
  2. 3 × 5 = 15
  3. Answer: 6x + 15

Substitution

Replace the letters with the numbers you're given, then work it out.

If a = 3 and b = 4, find 2a + b²:

  • 2 × 3 + 4² = 6 + 16 = 22

Try It Yourself

  1. Solve 5x + 2 = 27. (Answer: x = 5)
  2. Simplify 7a − 3b + 2a + 5b. (Answer: 9a + 2b)
  3. If x = 4, find the value of 3x² − 2x + 1. (Answer: 41)