How to solve simple linear equations using an easy to follow method.

When you are asked to solve an equation, you are trying to find the value of x (or any other letter), which balances both sides of the equation.

In order to be a good mathematician it’s important that you develop a proper method to solve equations, as this will make it easier when you get more difficult equations.

The best method to solve an equation, is to treat the equation like a “sea saw”. All equations have a Left Hand Side (LHS) and a Right Hand Side (RHS). Whatever you do to the LHS of the equation, you must also do the RHS, in order to keep the equation balanced. You will have to apply the inverse operations (in reverse order) to be able to solve an equation.

Let’s take a look at some examples now (The inverse operations have been put in brackets at the side of the working out).

Example 1

Solve x + 4 = 20

To find x, look at the LHS of the equation, and you will notice you are adding 4 to x.

The inverse (opposite) to add 4 is to take away 4, so you need to do this to both sides of the equation.

x + 4 = 20             (-4)

x=16.

Example 2

Solve 3x – 6 = 9.

This time on the LHS of the equation we are multiplying x by 3 and taking off 6. Therefore, we need to add 6, and then divide by 3 to both sides of the equation.

3x – 6 =9              (+6)

3x = 15                  (÷3)

X = 5

Example 3

Solve x/5 + 2 = 13.

This time on the LHS of the equation x is being divided by 5 and then 2 is being added. So we need to take away 2 from both sides of the equation, and times by 5.

x/5 + 2 =13          (-2)

x/5 = 11                (×5)       

x = 55

Extra Tips

Always do the inverses in reverse order.

Set your working out down the page(not across).

Check your final answer, by substituting your answer back into the original equation to see if it gives you the number on the RHS. To check that x = 55, in the last example, do 55/5 + 2, which gives 13 (the RHS). So x = 55 is correct.