Solving Proportions Using Cross Multiplication

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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

= (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 Â· 12

-12

= (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

x + 1 = 0

x = -1