Ever wondered how a market scale finds a missing weight?

At the market, a trader puts 2 identical bags of beans and a 4 kg weight on one side of a scale. It balances perfectly with 10 kg on the other side. How heavy is ONE bag? You can work it out — and that's exactly what solving an equation is.

📒 Solving Simple Equations: lesson notes

Use the balance idea to find the unknown in equations like 2x + 4 = 10.

An equation is a balance

In 2x + 4 = 10, the letter x stands for the number we don't know yet (one bag).

The = sign means both sides weigh the same — like a balanced scale.

To find x, we get it on its own. The golden rule: whatever you do to one side, do the same to the other side, so it stays balanced.

🔑 Key idea: Same change to BOTH sides keeps the equation true.

Worked example 1

Solve: 2x + 5 = 15

Step 1: Subtract 5 from both sides
2x + 5 = 15
2x + 5 − 5 = 15 − 5
2x = 10
Why? We want 2x on its own, so we remove the 5. Whatever we do to one side, we do to the other — like keeping a balance level.
Step 2: Divide both sides by 2
2x ÷ 2 = 10 ÷ 2
x = 5
Why? 2x means 2 × x. Dividing by 2 undoes the multiplication and leaves x alone.
Step 3: Check your answer
Put x = 5 back in: 2 × 5 + 5 = 15
✓ That matches 15, so the answer is right.

Answer: x = 5

What if there's a minus sign?

In 3x − 4 = 11, 4 has been taken away from 3x.

To undo taking away, we add. Add 4 to both sides: 3x = 15.

Then undo the multiplying by dividing both sides by 3: x = 5.

🔑 Key idea: Undo each step with its opposite: + ↔ −, × ↔ ÷.

Worked example 2

Solve: 3x − 4 = 11

Step 1: Add 4 to both sides
3x − 4 = 11
3x − 4 + 4 = 11 + 4
3x = 15
Why? We want 3x on its own, so we remove the 4. Whatever we do to one side, we do to the other — like keeping a balance level.
Step 2: Divide both sides by 3
3x ÷ 3 = 15 ÷ 3
x = 5
Why? 3x means 3 × x. Dividing by 3 undoes the multiplication and leaves x alone.
Step 3: Check your answer
Put x = 5 back in: 3 × 5 − 4 = 11
✓ That matches 11, so the answer is right.