Solving Equations
Solving Equations
In this video – we are going to be covering probably the most important topic in the Algebra syllabus… how to solve an equation.
When we talk about ‘solving’ an equation, it essentially means to rearrange the equation until you’ve got a value or an expression for the unknown.
The most common unknown in equations are represented by an ‘\(x\)’ but it can be anything.
Rearrange = Solve
In order to solve your equation, you simply need to make it the subject i.e. make it so that the equation reads as ‘\(x = …\)’.
The way that you rearrange these equations is to essentially move things from one side of the equals sign to the other by adding/subtracting/dividing/multiplying both side of the equation.
On paper, this sounds pointless but lets have a look at a quick example to help to understand this:
We want to solve \(2x + 1 = 3\)
So in order to make \(x\) the subject, we want to have all of our numbers on 1 side and our \(x\) on the other side.
To get rid of our \(+1\), we need to minus 1 from each side. This gives us:
\(2x = 3 – 1 = 2\)
So now we’ve got our \(2x = 2\), we need to divide both sides by 2 so that we are left with a single \(x\).
After dividing both sides by 2, we are left with \(x = 1\)… problem solved!
The key to solving almost any equation is to understand that you need to use addition to move negative numbers, subtraction to move positive numbers, multiplication to rearrange fractions, division to simplify numbers or separate numbers from an \(x\), and finally square roots to move squared numbers and visa versa.
Important point – when you square root a number, you need to remember that the answer could be positive or negative. e.g. \(\sqrt{25}\) could be either 5 or -5 as when we times a negative number with another negative number, we get a positive number.
If we’re given brackets, we want to multiply those out and ‘collect your terms’ which we covered in the ‘Multiplying Out Brackets’ video. Then rearrange and solve as we’ve just gone through.