An equation says two things are equal, and a letter like x stands for the number we do not yet know. To find x we get it on its own by undoing what has been done to it — using the inverse operation and doing the same to both sides. In x + 7 = 12, something is being added to x, so we subtract 7 from both sides: x = 12 − 7 = 5. Always check by putting your answer back in: 5 + 7 = 12. ✓ Adding when you should subtract is the classic slip.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- equation
- a statement that two amounts are equal
- inverse
- the opposite operation that undoes another
- solve
- find the value of the unknown letter
Worked examples
x + 7 = 12
- 1.Subtract 7 from both sides.
- 2.x = 12 − 7 = 5.
= 5
x + 4 = 9
- 1.Subtract 4 from both sides.
- 2.x = 9 − 4 = 5.
= 5
x + 6 = 15
- 1.Subtract 6 from both sides.
- 2.x = 15 − 6 = 9.
= 9
For parents
Method: Do the opposite to both sides.
What to say: Ask 'what has been done to x, and what undoes it?' then check by substituting back.
Common mistakes:
- Adding instead of subtracting (x + 7 = 12 → 19).
- Writing the total (12) or the added number (7) as the answer.