Suppose we wish to solve the equation
3x + 15 = x + 25
The important thing to remember about any equation is that the equals sign represents a balance.
What an equals sign says is that what’s on the left-hand side is exactly the same as what’s on the
right-hand side. So, if we do anything to one side of the equation we have to do it to the other
side. If we do this, the balance is preserved. The first step in solving this equation is to perform
operations on both sides so that terms involving x appear on one side only, usually the left. We can
subtract x from each side, because this will remove it entirely from the right, and give
2x + 15 = 25
We can subtract 15 from both sides to give
2x = 10
and finally, by dividing both sides by 2 we obtain
x = 5
So the solution of the equation is x = 5. This solution should be checked by substitution into
the original equation in order to check that both sides are the same. If we do this, the left is
3(5) + 15 = 30. The right is 5 + 25 = 30. So the left equals the right and the solution is correct.
Suppose we wish to solve the equation 2x + 3 = 6 − (2x − 3).
We first remove the brackets on the right to give
2x + 3 = 6 − 2x + 3
2x + 3 = 9 − 2x