A reason says which rule makes a step legal, for example “both sides must stay equal”. Saying why each step works is what lets you handle a question you have never seen.
The reason column
Write your working in two columns, the step on the left and the reason on the right. A worked example: solve 2x + 5 = 17.
| Step | Reason |
|---|---|
| 2x + 5 − 5 = 17 − 5 | Subtract 5 from both sides so the equation stays balanced |
| 2x = 12 | Simplify both sides |
| 2x ÷ 2 = 12 ÷ 2 | Divide both sides by 2 to leave x alone |
| x = 6 | Simplify |
Check: 2 × 6 + 5 = 17, which matches.
Move it across is not a reason
Some students learn “move the 5 across and change its sign”. It works, but it is a trick, not a reason. When the equation looks different, such as x ÷ 4 − 3 = 2, the trick gives no guide.
The balance reason does help. Add 3 to both sides to get x ÷ 4 = 5, then multiply both sides by 4 to get x = 20. One principle handles both equations.
Reasons in science answers
The same habit appears in Science. “The balloon shrinks” is a statement, but “the balloon shrinks because the air inside cools, so the particles move slower and collide with the walls less” is an explanation. The word “because” signals that a reason is present.
Where students lose marks
Two patterns lose marks. A correct answer with no reason, in a question that says “explain”, earns part marks at best. A reason that only repeats the step, such as “because I divided by 2”, does not count either.
The test is to ask whether the reason would still be useful on a different question. A rule does, and a repeat of the action does not.
Try it yourself
Solve 3(x − 2) = 15 and write a reason beside each step.
Answer
Divide both sides by 3 to undo the multiplication: x − 2 = 5. Add 2 to both sides to isolate x: x = 7.
Check: 3 × (7 − 2) = 3 × 5 = 15, which is correct. You could also expand first, 3x − 6 = 15, but the divide-first route needs fewer lines.
Next steps
The next skill is recognising an assumption. For more equation practice, see solving a linear equation step by step. With SPM Mathematics tuition, a teacher can ask you why, line by line.