To sum up then, in general we can add, subtract, multiply and divide when manipulating equations, as long as we do the same thing to both sides. Sometimes it is necessary to carry out several operations, one after the other.
If more than one operation is to be carried out, it is important to know which one should be done first. The answer may be different if you carry out the operations in another order! For example, in the following expression no brackets have been used and it is ambiguous.
2 x 32.
Either we could multiply 2 by 3 and then square the result, or we could square 3 first and then multiply the result by 2. The first calculation would give the answer 36, while the second calculation would give 18. By using brackets we can specify which operation is to be carried out first.
(2 x 3)2
and
2 x (32).
The rule is: we must always carry out the operation in brackets first.