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Multiplying and dividing both sides

A number is written right in front of x.

What it looks like

2x = 8

2x means 2 times x. There is no times sign. Two lots of x make 8.

To get x on its own, divide by 2. Dividing undoes multiplying.

Worked example 1

  1. 2x = 8

  2. Divide both sides by 2

  3. x = 4

Check it: 2 times 4 is 8. It works.

Worked example 2

This time x has been divided.

  1. x ÷ 3 = 5

  2. Multiply both sides by 3

  3. x = 15

The answer is bigger than the number you started with. That is fine. Check it: 15 ÷ 3 is 5.

The most common mistake

Subtracting the number in front of x.

Not this

2x = 8, subtract 2 from both sides

2x − 2 = 6

The 2 in front of x is still there.

This

2x = 8, divide both sides by 2

x = 4

The 2 is multiplying x. Only dividing undoes it.

In the game

You meet these puzzles in the Ice Keep.

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