An equation states that two expressions are equal. A solution is a value that makes that statement true. Think of the two sides as a balance: adding, subtracting, multiplying or dividing by the same permitted quantity on both sides preserves the balance.
Undo operations in a sensible order
In 3x + 5 = 20, subtract 5 from both sides before dividing by 3. This gives 3x = 15, so x = 5. Writing the operation on both sides helps prevent sign errors that can happen when terms appear to ‘move’ without explanation.
If brackets are present, distribute multiplication carefully. For instance, 2(x + 3) = 2x + 6, not 2x + 3.
- Division by zero is never allowed.
- A coefficient such as 3 in 3x means multiplication: 3 × x.
Translate and then check
For a word problem, define the unknown before writing an equation. ‘Five more than twice a number is 19’ becomes 2x + 5 = 19. Avoid changing the meaning of the words to fit a favourite operation.
Substitute the solution into the original equation, including all brackets. Both sides should have the same value. In a real situation, also check that the answer makes sense for what is being counted or measured.
Put it into practice
A worked example
Solve 4(x − 2) = 20.
- Divide both sides by 4: x − 2 = 5.
- Add 2 to both sides: x = 7.
- Check the original equation: 4(7 − 2) = 4 × 5 = 20.
Answer: x = 7.
Try it yourself
Have a go before revealing the answer.
Solve 5x − 3 = 22.
Show answer
5x = 25, so x = 5.
Answer: 5x = 25, so x = 5.
Three equal notebooks and a ₹10 pen cost ₹85. Find the notebook price.
Show answer
Let one notebook cost ₹x. Then 3x + 10 = 85, so x = 25. Each notebook costs ₹25.
Answer: Let one notebook cost ₹x. Then 3x + 10 = 85, so x = 25. Each notebook costs ₹25.
Watch out for these
- A minus sign outside brackets changes every sign inside when the brackets are removed.
- Check the original equation, not just the final rearranged line.
Continue with official resources
Match these concept notes to your current textbook and syllabus. They are independent explanations, not official board publications.
