Linear equations · Year 9
In Year 9 you learn: equations with brackets and fractions.
A linear equation has an unknown, usually x, with no powers — like 3x + 5 = 20. Solving it means finding the value that makes both sides equal. Think of a balance: whatever you do to one side, you must do to the other.
Key facts
- Do the same thing to both sides to keep the equation balanced.
- Undo the operations in reverse order: for 3x + 5 = 20, subtract 5 first, then divide by 3.
- If x is on both sides, subtract the smaller x term from both sides first.
- With brackets, expand first (or divide both sides by the number outside).
- With fractions, multiply every term by the denominator (or the LCM of the denominators).
- Check your answer by substituting it back into the original equation.
Worked examples
Example 1
Solve 4x − 7 = 21.
Answer: x = 7
Example 2
Solve 5x + 3 = 2x + 18.
Answer: x = 5
Example 3
Solve 3(2x − 1) = 4(x + 2).
Answer: x = 5.5
Example 4
Solve (x + 4)/3 = (2x − 1)/5.
Answer: x = 23