3.7 Solving Equations Involving only Multiplication and Division
In the previous section you saw how subtracting undid an addition and vice versa, because adding and subtracting are inverse operations.
This next section involves only multiplication and division. I hope you remember that each is the inverse operation of the other. So to undo a multiplication we will be dividing. And vice versa.
First of all, some algebraic conventions.
| Convention 1: | Unless it will lead to confusion, all multiplication signs will
be omitted. Thus ab means a ´ b and pqr means p ´ q ´ r. |
| Convention 2: | Since multiplication is commutative, the order of variables does
not matter, although alphabetical order is preferable. Thus bca is the same as cab but abc is best of all. |
| Convention 3: | If a number is involved in multiplying, it always comes first. Thus you write 4x and not x4 to mean ‘4 times x’. |
| Convention 4: | In addition/subtraction, you can only simplify like terms, or
terms which look alike. With multiplying, however, you can simplify virtually anything.
Thus |
