Equations

We talked about equations at the start of the course in the Number Line lesson. This is how we defined an equation:

An equation is a statement in maths that shows that two expressions are equal. An expression is a number or a combination of numbers and mathematical symbols.

The word equation comes from the word equal which means the same as.

A symbol is something that represents something else.

Some examples of symbols are:

The recycle symbol

All of the symbols above represent something but aren’t the something that they represent. The word “apple” isn’t an apple, for example. It stands in place of, or stands for, a real apple in writing and speech.

In equations, we use symbols to represent operations…

+, -, ÷, ×

…and symbols to represent numbers…

x, y

…and relationships

=, >, <

You know what all of the operation symbols stand for and you know the equals symbol (=) and greater than (>) and less than (<) symbols.

Here we will look at the x and y symbols.

In the equations below, these symbols represent unknown numbers.

$3x = 9$

$4y = 3x - 1$

These are two mathematical equations. Let’s solve these equations. This means, let’s work out what the value of $x$ and $y$ are. Let’s find out what numbers they represent.

We need to work out $x$ first because there is only one unknown ( $x$ ) in $3x = 9$ . When there are two unknowns in an equation, we don’t have enough information to calculate what the unknowns stand for. We can’t solve what number $y$ is in $4y = 3x - 1$ until we know what $x$ is.

To work out what $x$ is, we need to get $x$ on its own. Another way to say this is we have to make $x$ the subject of the equation.

To get $x$ on its own, we need to divide it by three. If we do something to one side of an equation, to keep the equation equal, we need to do the same to the other side.

$3x = 9$

$x = \frac{9}{3}$