 Solving equations means finding the value of the number represented by a letter in an equation, so your final answer will look something like: x = 4. The method we use is often called the balance method. Simply imagine the equation as a set of old fashioned scales, with the equals sign as the pivot. We keep the equation in balance – while simplifying to your answer – by doing the same operations to both sides until you have your final answer.

Essentially you need to “strip away” all of the numbers from around the letter you’re finding by doing the opposite of the number’s operation (so if you have a minus then you need to add to both sides). Do the same thing to both sides of the equation to keep everything balanced. You do this process in the reverse order to BIDMAS, until all that’s left is the final answer. It’s much easier to understand when you see this process working to answer a question, so let’s look at an example…

Got it? Okay, let’s move on to a harder one…

## Solving equations with letters on both sides

Equations get a bit harder when you have letters on both sides of the equals sign. With these ones you need to add in an extra step at the start – you need to bring the letters together on one side of the equation by adding or subtracting the same number or letters to both sides. Remember that whatever you do to one side of the equation you must do to the other side as well. Always try to keep your letters positive (it makes it much easier!). For example:

With this method for solving equations you can solve any linear equation they give you (a single equation with just one unknown and no indices with the letter). There are other, more challenging types of equations that you need to know about, including quadratic equations and simultaneous equations; but don’t worry, we’ve got you covered with other thorough revision guides on these topics. Simply follow the links to revise each of these types of equations.

## Practice Questions

Solve the following equations:

1. 4x = 24
2. x + 5 = 11
3. 2a – 3 = 7
4. 2x + 5 = 9
5. 3y – 2 = 25
6. x/2 + 5 = 12
7. 3(x+4) = 18
8. 3x + 2 = x + 8
9. 2x + 5 = 4x – 3
10. 5(y + 7) = 3(2y + 5)
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