Solve multi-step proportions

Learn how to solve multi-step proportions easily with a couple of good examples.

Quick review:

Suppose you have the following proportion:

Numerator #1 / Denominator #1 = Numerator #2 / Denominator #2 

After doing cross-multiplication, it is equivalent to 

Numerator #1 × Denominator #2 = Numerator #2 × Denominator #1

Example #1

Solve the proportion (x - 5) / 4 = (x + 3) / 6

(x - 5) / 4 = (x + 3) / 6

The proportion is equivalent to 

(x - 5) × 6 = (x + 3) × 4

(x - 5) × 6 = (x + 3) × 4

Use the distributive property

6x - 30 = 4x + 12

Subtract 4x from each side of the equation

6x - 4x - 30 = 4x - 4x + 12

2x - 30 = 0 + 12

2x - 30 = 12

Add 30 to each side of the equation

2x - 30 + 30 = 12 + 30

2x + 0 = 42

2x = 42

Divide each side by 2

2x/2 = 42/2

x = 21

Example #2

Solve the proportion 3 / (x - 4) = -5 / (4x + 1)

3 / (x - 4) = -5 / (4x + 1)

The proportion is equivalent to 

3 × (4x + 1) = -5 × (x - 4)

3 × (4x + 1) = -5 × (x - 4)

Use the distributive property

12x + 3 = -5x + 20

Add 5x to each side of the equation

12x + 5x + 3 = -5x + 5x + 20

17x + 3 = 0 + 20

17x + 3 = 20

Subtract 3 from each side of the equation

17x + 3 - 3 = 20 - 3

17x + 0 = 17

17x = 17

Divide each side by 17

17x/17 = 17/17

x = 1

Recent Articles

  1. Types of Triangles

    Dec 03, 22 12:47 PM

    Learn to identify 6 types of triangles based on their sides or angles and 7 more types based on both their sides and angles.

    Read More

  2. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes