Algebra — It’s Just Missing Numbers
If you can work out “? + 3 = 7” then you can do algebra. The only difference is we use letters instead of question marks. That’s genuinely it.
Letters Are Mystery Numbers
When you see x + 3 = 7, x is just a number we don’t know yet. Our job is to figure out what it is. In this case x = 4 because 4 + 3 = 7.
Letters like x, y, n are just placeholders. They aren’t scary — they’re just gaps to fill in.
Key Rules
- Whatever you do to one side of an equation, you must do to the other side.
- 2x means 2 × x | x² means x × x
- Like terms have the same letter and power: 3x and 5x are like terms; 3x and 3x² are NOT.
Solving Simple Equations (The Balancing Scales)
Think of an equation like a set of balancing scales. Both sides weigh the same. If you take something off one side, you have to take the same off the other side to keep it balanced.
Worked Example
Solve: 2x + 5 = 13
- Subtract 5 from both sides: 2x = 8
- Divide both sides by 2: x = 4
Check: 2(4) + 5 = 8 + 5 = 13 ✓
Collecting Like Terms
You can only combine terms that have the same letter and power. Think of it like sorting fruit: you can add apples to apples, but not apples to bananas.
Worked Example
Simplify: 3x + 2y + 5x − y
- x terms: 3x + 5x = 8x
- y terms: 2y − y = y
- Answer: 8x + y
Expanding Brackets
Multiply everything inside the bracket by the number (or letter) outside. Every term, no exceptions.
Worked Example
Expand: 3(2x + 4)
- 3 × 2x = 6x
- 3 × 4 = 12
- Answer: 6x + 12
Substitution
Substitution means replacing the letter with a number and working out the answer. Put the number in brackets to avoid sign errors.
Worked Example
If x = 3, find the value of 4x² − 2x + 1
- 4(3)² = 4 × 9 = 36
- −2(3) = −6
- 36 − 6 + 1 = 31
Common Mistakes
- Only doing an operation on one side of the equation.
- Combining unlike terms (e.g. adding 3x and 2x²).
- Forgetting to multiply every term inside the bracket.
- Squaring first and then substituting a negative (always use brackets!).
Practice Questions
- Solve: 5x − 3 = 22
- Simplify: 7a + 3b − 2a + 5b
- Expand: 4(3y − 2)
- If x = 5, find 2x² + 3x − 4
- Solve: 3(x + 2) = 21
Answers: 1) x = 5 2) 5a + 8b 3) 12y − 8 4) 61 5) x = 5