# 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.

## 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?

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