# Solving equations

Solving an equation results in finding the value of the variable to make the equation true. In simple equations we can ‘guess and check’ to find the solution. For example, To make this equation true must be since .

The method to solve any equation algebraically uses opposite operations (inverses), performed to both sides of the equation to keep the equation ‘balanced’.

To use this method remember that:

- Adding and subtracting are the inverse (or opposite) of each other
- Multiplying and dividing are the inverse of each other

*e.g.*

Subtract to both sides to undo the

Divide both sides by to undo the

The answer is

## Unknowns of both sides

Some equations have variables on each side of the equal sign, for example .

Solve this equation by rearranging all the variables onto one side of the equation and all the numbers onto the other side.

*e.g.*

Subtract from both sides. This will result in moving all the s to the left of the equal sign

Subtract from both sides to move the to the right of the equal sign

Divide both sides by to isolate the

The equation has the solution

## Further information

- Press the Printer Friendly button at the top left-hand corner to download a printable handout
- View Khan Academy’s videos to watch an explanation of worked example and a set of practice problems