Equations with brackets

A number sits in front of some brackets.

What it looks like

2(x + 3) = 10

2(x + 3) means 2 times everything inside the brackets. Divide both sides by the number in front.

The brackets fall away. What is left is a puzzle you already know.

Worked example 1

  1. 2(x + 3) = 10

  2. Divide both sides by 2

  3. x + 3 = 5

  4. Subtract 3 from both sides

  5. x = 2

Check it: 2 + 3 is 5. Then 2 times 5 is 10. It works.

Worked example 2

This one takes three spells.

  1. 3(2x + 4) = 18

  2. Divide both sides by 3

  3. 2x + 4 = 6

  4. Subtract 4 from both sides

  5. 2x = 2

  6. Divide both sides by 2

  7. x = 1

An answer of 1 can look too small. It is right.

Check it: 2 times 1 is 2. Then 2 + 4 is 6. Then 3 times 6 is 18.

The most common mistake

Going for the number inside the brackets first.

Not this

2(x + 3) = 10, subtract 3 from both sides

2(x + 3) − 3 = 7

The 3 inside the brackets has not gone.

This

2(x + 3) = 10, divide both sides by 2

x + 3 = 5

You cannot reach inside the brackets while a number is in front of them. Deal with the number in front first.

In the game

You meet these puzzles in the Crystal Caverns.

Back to the game