Changing the subject of an equation
When the letter you want to find is not on its own, you need to rearrange the equation and make your letter the subject of the equation before you can solve it.
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!
We are going to use the method:
Change side, change operation
Example
Solve the equation \(x + 5 = 12\).
Answer
To find \(x\) you need to get rid of the \(+ 5\).
\(x + 5 = 12\)
To get rid of \(+5\) you have to do the opposite, \(-5\).
If you do this to one side of the equation, you also have to do it to the other.
\(x + 5 - 5 = 12 - 5\)
The \(+5\) and \(-5\) on the left cancel each other out, leaving a simple subtraction:
\(x = 12 - 5\)
\(x = 7\)
The quick way of looking at this is to say that + on the left has changed side and changed operation to become - on the right
Question
Solve the equation \(3x - 15 = 9\)
To make \(x\) the subject you have to get rid of the \(-15\) on the left. This changes side and changes operation to become \(+15\) on the right.
To get rid of the \(3\) (which means \(\times 3\)) on the left, you change side and change operation so that it becomes \(÷ 3\) on the right:
Subtract becomes add and multiply becomes divide.
