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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, 4 + N = 10  To make this equation true N must be 6 since 4 + 6 = 10.

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


2N + 3 = 7   Subtract 3 to both sides to undo the + 3

2N = 4          Divide both sides by 2 to undo the \times 2

N= 2            The answer is N=2

Unknowns of both sides

Some equations have variables on each side of the equal sign, for example 6N + 3 = 4N + 13.

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


6N + 3 = 4N + 13    Subtract 4N from both sides. This will result in moving all the Ns to the left of the equal sign

2N + 3 = 13              Subtract 3 from both sides to move the +3 to the right of the equal sign

2N = 10                     Divide both sides by 2 to isolate the N

N = 5                        The equation has the solution N= 5

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