Bitesize has changed! We're updating subjects as fast as we can. Visit our new site to find Bitesize guides and clips - and tell us what you think!

Did you know?

We also have Bitesize study guides covering many subjects at National 4 and National 5 on our Knowledge & Learning BETA website.

Home > Maths I > Relationships > Simple equations and inequalities

Maths I

Simple equations and inequalities

Back

Solving equations

Introduction

Problems are often answered in mathematics by solving equations.

To solve them, we need to find what number the letter in the equation represents. That number is called the solution of the equation.

There are usually several ways to solve an equation. If the method you choose to use always gives you the correct answer, then keep using this method!

To get some practise at solving equations, try to follow the worked examples below.

Example 1

Solve {x + 7 = 12}.

This is the simplest type of equation to solve.

What number added to 7 equals 12?

The answer is 5 (because 5 + 7 = 12).

Therefore, x = 5 is the solution.

Example 2

Solve y - 4 = 10.

This is very similar to Example 1.

What number minus 4 equals 10?

The answer is 14 (because 14 - 4 = 10).

Therefore, y = 14 is the solution.

Example 3

Solve 3x = 5.

This is a different type of equation from the first two.

3 times a number represented by x is equal to 5.

To find x, divide both sides by 3.

So, x = \frac{5}{3} is the solution.

Example 4

Solve 4y + 3 = 11.

This equation is like Example 1 and Example 3 combined.

What number added to 3 equals 11?

The answer is 8 (because 8 + 3 = 11).

Therefore, 4y = 8, i.e.

4 times y equals 8.

To find y, divide both sides by 4:

y = \frac{8}{4} = 2.

The solution is y = 2.

Example 5

Solve 16 - 2x = 6.

Add 2x to each side:

16 = 6 + 2x.

Re-order the equation:

6 + 2x = 16,

2x + 6 = 16.

Subtract 6 from each side:

2x = 10.

To find x, divide both sides by 2.

Therefore, x = 5 is the solution.

Now, try to solve these equations.

Question

Solve a + 3 = 8

Answer

a = 5 (because 5 + 3 = 8)

Question

Solve 6 - m = 1

Answer

m = 5 (because 6 - 5 = 1)

Question

Solve 4y = 9

Answer

y = \frac{9}{4}

Question

Solve 2x - 3 = 6

Answer

x = 9/2 (because 2x = 9)

Question

Solve 14 - 3n = 8

Answer

n = 2 (because 14 - 6 = 8, 3n = 6)

Well done if you got the right answers! If you didn't, check through the answers again.

Back

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.