Solve equations with unknowns on both sides

Home learning focus

Learn about solving equations where an unknown, such as x, appears on both sides of the equals sign.

This lesson includes:

  • two videos
  • a learning summary
  • three activities with answers

Learn

Equations

An algebraic equation will always contain an unknown value and an equals sign. The unknown value is represented by a symbol, for example x, y or z.

Solving an equation means finding the value of the unknown by performing the same operation on each side of the equals sign.

Quickly refresh your knowledge of solving equations by watching this short video from BBC Bitesize, KS3 Maths.

Find out how to solve simple algebraic equations with one unknown

Solving more complex equations - unknowns on both sides of the equals sign

Sometimes an equation will have unknowns on each side of the equals sign, for example 2x + 2 = x + 4.

As with other equations with multiples of an unknown (in this case 2x and x) and other numbers (2 and 4), your aim is to get all the unknowns onto one side and all the numbers onto the other.

The equation 2x + 2 = x + 4 can be represented in this diagram. The bags in the image represent the unknown value (x) and the sweets represent the numbers in the equation.

You need to get the unknown value on just one side of the equation, so begin by subtracting x (taking one bag away) from each side, as shown here.

Written algebraically, this gives you x + 2 = 4

Now you have the type of equation that you should recognise, so all you need to do is subtract 2 from both sides.

This gives you x = 2 as your solution.

Check:

Substituting x = 2 back into the original equation (2x + 2 = x + 4) allows you to make sure your working out is correct.

(2 × 2) + 2 = 2 + 4 can be simplified to:

4 + 2 = 2 + 4, and further to:

6 = 6

The equation balances, so x = 2 is the correct solution.

Video - Teacher Talk: Solving equations

For more help and advice with solving equations with unknowns on both sides of the equals sign, watch this Teacher Talk video, beginning at 2:01. There are many more Teacher Talks covering different Maths topics on BBC iPlayer.

The last example in the video (4a - 1 = 2a + 11) looks at what you have to do when a number is being subtracted from an unknown on one side of the equals sign - if this is a process you're less confident with, you can see a full explanation of how to find the solution here.

Teacher Talks: Solving equations

Practise

Activity 1

Quiz

How much do you know about unknowns in equations? To get you thinking, have a go at this short quiz. One of the questions needs you to expand brackets to find the solution - click here if you need a recap on how to do this.

Activity 2

Pairs activity

Now have a go at this pair-matching activity from Oxford University Press to push your skills in unknowns in equations further. Try to complete the challenge in as few attempts as possible! You can check your answers within the activity.

Pair-matching activity - Equations with unknowns on both sides

Activity 3

Working with more complex equations - Practise

Keep going: now try the mixed-practice questions in this worksheet from Hodder to test your knowledge further. Write your answers on a piece of paper.

Working with more complex equations

Click here for the answer sheet.

There's more to learn

Have a look at these other resources around the BBC and the web.

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