Solving Equations
Using Multiplication and Division
After studying this lesson, you will be able to:
- Solve equations using multiplication and division.
Review of Steps for Solving Equations:
1. Remove parentheses by multiplying (this step is not always
necessary)
2. Collect like terms on each side of the equal sign
3. Isolate the variable by undoing the operation
4. Check by substituting the solution into the original
equation
Example 1
 |
This equation can be solved by cross
multiplying. |
| 56 = 7a |
Use cross multiplication to create a new
equation. (4 times 14 and 7 times a) |
 |
To isolate the variable we have to
"undo" the 7 times a. The opposite of
multiplication is division, so we divide each side by 7 |
| 8 = a |
56 divided by 7 is 8 and 7a divided by 7
is a |
Example 2
Check:
substitute  for 4 y 4 in the equation where we
converted to improper fractions
Example 3
| 10p = -100 |
Since 10 is multiplied by p, we need to
"undo" the operation by dividing by 10 |
 |
Both sides are divided by 10 |
| p = -10 |
|
Check by substituting -10 in the original equation
10 (-10) = -100
-100 = -100
|
multiplied by y, we need to "undo"
by dividing 
