How to solve simple algebraic equations

  • An equation is a mathematical expression that contains an equals symbol.

  • Equations often contain algebra. Algebra is used in Maths when we do not know the exact number in a calculation - this unknown value can be replaced with a letter.

  • We solve an equation by working out the value for one letter. To solve an equation we use the inverse operations to undo the equation.

Find out how to solve simple algebraic equations with one unknown

Have a go

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Operations

An operation is a mathematical process. Common examples are addition (+), subtraction (-), multiplication (x) or division (÷).

An inverse operation is the opposite of the operation used in the equation.

+ is the opposite of -

- is the opposite of +

x is the opposite of ÷

÷ is the opposite of x

Writing an equation

Let's turn the problem below into an equation.

3 loaves of bread and a £4 pack of cheese cost £10. How much is each loaf?

In this equation we want to work out the cost of one loaf of bread.

As the cost of bread is the unknown, we will represent this with a x.

We need 3 loaves of bread, so in our equation we will represent this with 3x.

We know the cheese costs £4 and the total spend is £10.

So now we can write our equation:

3x + 4 = 10

Solving an equation

When solving an equation it is important to find the value of one letter.

Let's solve the equation 3x + 4 = 10

  • To remove the + 4 we complete the inverse (opposite) operation by subtracting the 4.

    3x = 10 – 4

  • That gives us 3x = 6 (3 loaves cost £6)

  • To work out the cost of one loaf we divide both sides of the equation by 3.

  • x = 6 ÷ 3

  • So x = 2 (one loaf costs £2)

Algebraic equations quiz

Test your knowledge with this quick quiz.

Where next?

Discover more about this topic from around Bitesize.

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