What is an equation?

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

Equations often contain algebra, where a letter is used to replace an unknown value.

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.

This video shows a visual method for solving a word problem. The method uses a bar model where the letter \(x\) stands for the unknown value we need to find.

Find out how to solve simple algebraic equations with one unknown

Have a go:

The bar model used in the video is very close to creating an equation to solve the problem. Read through the steps below to see how similar the two methods are.

Both methods start in the same way, working out the key information in the word problem:

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

Bar model

Equation

Step 1

Draw a bar model to represent the first part of the problem.

Draw a bar with one length of \(3x\) and one length of \(4\).

Draw another bar of equal length marked \(10\)

Step 1

Use the information in the word problem to create an equation.

\[3x + 4 = 10\]

Step 2

Remove the \(4\) (the price of the pack of cheese) from the end of the bar model

Subtract \(4\) from \(10\) to match this. \(10-4=6\)

Step 2

Subtract \(4\) from each side of the equation.

\[3x + 4 (-4) = 10 (-4)\]

\[3x = 6\]

Step 3

Find the value of one \(x\).

Remove \(\frac{2}{3}\) of the length of each bar.

This leaves a single \(x\) and \(6 \div 3\) which equals \(2\).

Step 3

Find the value of \(x\).

Divide both sides of the equation by \(3\)

\[\frac{3x}{3} = \frac{6}{3}\]

\[x = 2\]

Step 4

Put in the correct units

The problem is about money, so the answer isn't just a number. It needs to be in pounds.

\(x = £2\).

Step 4

Put in the correct units

The problem is about money, so the answer isn't just a number. It needs to be in pounds.

\(x = £2\).