Years 7–9 · Mathematics
Algebra basics: expressions, substitution and solving equations
Algebra uses letters (called variables or pronumerals) to stand for numbers we don't know yet, or numbers that can change. It lets us write general rules and solve problems systematically.
Stuck? Ask the free AI tutor
Try asking: “How do I solve 2x + 3 = 11?”
Expressions and terms
3x + 5 is an expression. 3x means 3 × x. The 3 is called the coefficient, and 5 is a constant term.
Like terms have the same variable part and can be combined: 4x + 2x = 6x, but 4x + 2 cannot be simplified further.
Substitution
Substituting means replacing the variable with a number. If x = 4, then 3x + 5 = 3 × 4 + 5 = 17.
Expanding brackets
Multiply the number outside by every term inside: 3(x + 4) = 3x + 12.
Solving equations with the balance method
An equation says two things are equal, like a balanced scale. Whatever you do to one side, do to the other. Undo operations in reverse order until the variable is alone, then check by substituting back in.
Worked examples
Solve 2x + 3 = 11
- Subtract 3 from both sides: 2x = 8.
- Divide both sides by 2: x = 4.
- Check: 2 × 4 + 3 = 11 ✓
Answer: x = 4
Solve 5x − 7 = 18
- Add 7 to both sides: 5x = 25.
- Divide both sides by 5: x = 5.
- Check: 5 × 5 − 7 = 18 ✓
Answer: x = 5
Expand 4(2x − 3)
- 4 × 2x = 8x.
- 4 × −3 = −12.
Answer: 8x − 12
Common mistakes to watch for
- Only doing an operation to one side of the equation.
- Writing 3x as 3 + x instead of 3 × x.
- Forgetting to multiply every term inside the brackets when expanding.
Practice questions
Try these, then reveal the answers. For more questions with hints, use the tutor.
1. If a = 6, what is 4a − 9?
Show answer
15
2. Solve x + 9 = 23
Show answer
x = 14
3. Solve 3x = 27
Show answer
x = 9
4. Solve 4x + 1 = 29
Show answer
x = 7
5. Expand 5(x + 2)
Show answer
5x + 10