Rearranging Formulas
Rearranging Formulas
In this video we are going to be learning about Rearranging Formulas. This is EXTREMELY similar to Solving Equations so I would suggest watching that video first.
The difference between Rearranging Formulas and Solving Equations is of the question asking you to ‘solve’ or ‘find \(x\)’, it will ask you to make a certain letter the subject.
The way you do this is exactly the same as solving the equation but instead of making \(x\) the subject, you make whatever letter the question asks for, the subject.
This sounds relatively straight forward but some of the questions that can be thrown at you are a bit nasty.
Let’s get into how they can be nasty and how we can beat them.
Subject appears more than once
An example could be \(y = \frac{x+1}{x-1}\) – make $x$ the subject.
Well, we know we need to be left with a single $x$ on one side of the equals sign so let’s get stuck in and see how it goes.
Our first step would be to get rid of the fraction – we multiply both sides by \(x-1\) which will leave us with \(y(x-1)=x+1\)
We then multiply out the brackets to give us \(yx-y=x+1\).
Next we get rid of our single \(y\) by adding it to both sides —> \(yx=x+y+1\)
Then we bring the \(x\) across to the other side so we have all of the \(x\)s on 1 side —> \(yx – x=y+1\)
Now we can factorise the left side of our equation to leave us with \(x(y-1)=y+1\)
Finally, we can divide both sides by \((y-1)\) which gives us our final answer of \(x = \frac{y+1}{y-1}\).
Subject appears as a fraction
An example could be \(x = \frac{3y+2}{5}\) – make \(y\) the subject. What do we do?
If you watched the Solving Equations video, you’ll know that if we want to get rid of a fraction, we multiply. If we multiply both sides by 5, we are left with
\(5x = 3y+2\).
Next we get rid of the 2 by subtracting 2 from both sides, leaving us with \(5x-2 = 3y\).
Finally, we divide both sides by 3 to leave us with \(y = \frac{5x-2}{3}\) – this is our answer. Simple enough, eh?
Question includes squares/square roots
As we know, squares and square roots are the inverse of each other so if we have a square that we want to be removed, we know we need to apply a square root to both sides and visa versa. We can also explore some examples of these as well.