Solving Proportions Using Cross Multiplication
Example 1
Solve the proportion for w:
| Solution
|
 |
 |
| Cross multiply.
Distribute the 6.
Subtract 6w from both sides.
Divide both sides by 4.
|
10w 10w
4w
w |
= (w + 4)6 = 6w + 24
= 24
= 6 |
We leave the check to you.
Example 2
Solve the proportion for x:
| Solution |
 |
 |
| Cross multiply.
Simplify.
This is a quadratic equation.
We write it in standard form.
Factor the right side. |
-1 ยท 12
-12
0
0 |
= (x + 3)(x - 5) = x2 - 2x - 15
= x2 - 2x - 3
= (x - 3)(x + 1) |
| Use the Zero Product Property.
Solve each equation.
We leave the check to you. |
x - 3 = 0 x = 3 |
or
or |
x + 1 = 0 x = -1 |
