SIMPLE EQUATION

Notice that in each case above, opposite operations are used; that is, if the equation has addition, you subtract from each side.

• Multiplication and division equations:

Some equations involve only multiplication or division. This is typically when the variable is already on one side of the equation, but there is either more than one of the variable, such as 2 x, or a fraction of the variable, such as

 or 

In the same manner, as when you add or subtract, you can multiply or divide both sides of an equation by the same number, as long as it is not zero, and the equation will not change.

Example 4:

Solve for x.

3 x = 9

Divide each side of the equation by 3.

To check, replace x with 3:

Example 5:

Solve for y.

To solve, multiply each side by 5.

To check, replace y with 35:

Example 6:

Solve for x.

To solve, multiply each side by .

Or, without cancelling,

Notice that on the left you would normally not write  because it would always cancel to 1x or x.

• Combinations of operations:

Sometimes you have to use more than one step to solve the equation. In most cases, do the addition or subtraction step first. Then, after you’ve sorted the variables to one side and the numbers to the other, multiply or divide to get only one of the variables (that is, a variable with no number, or 1, in front of it: x, not 2 x).

Example 7:

Solve for x.

2 x + 4 = 10

Subtract 4 from both sides to get 2 x by itself on one side.

Then divide both sides by 2 to get x.

To check, substitute your answer into the original equation: