Solve Equations with Brackets

When we solve algebraic equations, our aim is to end up with one letter on one side of the equals sign and one number on the other.  This is the solution.

We do this by using inverse operations to undo things that get in the way, but remember that we must do the same thing to both sides.

When brackets are involved, we multiply out the brackets first.

If you need a reminder of how to do this, why not have a look at the activity called 'Multiply Out Double Brackets and Simplify'

Example

7(b + 3) - 2(b - 3) = 47

Answer

Multiply out each set of brackets - be very careful with the negative signs! Remember that two negatives make a positive! (-2 x -3 = + 6)

7b + 21 - 2b + 6 = 47

Simplify by collecting like terms.

5b + 27 = 47

Subtract 27 from both sides.

5b + 27 - 27 = 47 - 27

Simplify

5b = 20

Divide both sides by 5

5b ÷ 5 = 20 ÷ 5

Simplify

b = 4

Want a bit more help with this before you begin? Why not watch this short video?