🧱 See It
Picture a balance scale. On the left side sits a mystery bag (it holds some number of blocks, but you can't see how many) plus 3 loose blocks. On the right side sit 7 loose blocks. The scale is perfectly level — both sides weigh exactly the same.
Mystery bag + 3 blocks = 7 blocks. What's in the bag?
✏️ Draw It
To find the mystery bag's weight without opening it, remove the same number of blocks from both sides. The scale stays balanced no matter what, as long as you do the exact same thing on each side.
Take 3 blocks off each side — the mystery bag is left alone on the left, and 4 blocks remain on the right.
The bag weighs 4.
🔢 Write It
The mystery bag is written as a letter, usually x. The picture above becomes:
x + 3 = 7
Subtract 3 from both sides — same move as taking 3 blocks off each pan:
x + 3 − 3 = 7 − 3
x = 4
💡 Worked Examples
Example 1 — Addition: x + 5 = 12
- Goal: get
xalone. - Subtract 5 from both sides:
x + 5 − 5 = 12 − 5 - Answer:
x = 7
Example 2 — Multiplication: 4x = 20
Here 4x means "4 mystery bags." All 4 bags together weigh 20, so each bag weighs a quarter of that.
- Goal: get one
xalone. - Divide both sides by 4:
4x ÷ 4 = 20 ÷ 4 - Answer:
x = 5
🧠 Quick Reference
| If the equation has… | Undo it with… |
|---|---|
x + a = b | Subtract a from both sides |
x − a = b | Add a to both sides |
a·x = b | Divide both sides by a |
x ÷ a = b | Multiply both sides by a |
Addition and subtraction undo each other. Multiplication and division undo each other.