Properties of inequality


We will show 6 properties of inequality. When appropriate, we will illustrate with real life examples of properties of inequality.






Let x, y, and z represent real numbers

Addition property:

If x < y, then x + z < y + z

Example: Suppose Sylvia's weight < Jennifer's weight, then Sylvia's weight + 4 < Jennifer's weight + 4

Or suppose 1 < 4, then 1 + 6 < 4 + 6

If x > y, then x + z > y + z

Example: Suppose Sylvia's weight > Jennifer's weight, then Sylvia's weight + 9 > Jennifer's weight + 9

Or suppose 4 > 2, then 4 + 5 > 2 + 5

Subtraction property:

If x < y, then x − z < y − z

Example: Suppose Sylvia's weight < Jennifer's weight, then Sylvia's weight − 4 < Jennifer's weight − 4

Or suppose 4 < 8, then 4 − 3 < 8 − 3

If x > y, then x − z > y − z

Example: Suppose Sylvia's weight > Jennifer's weight, then Sylvia's weight − 9 > Jennifer's weight − 9

Or suppose 8 > 3, then 8 − 2 > 3 − 2

Multiplication property:

If x < y, and z > 0 then x × z < y × z

Example: Suppose 2 < 5, then 2 × 10 < 5 × 10 ( Notice that z = 10 and 10 > 0)

If x > y, and z > 0 then x × z > y × z

Example: Suppose 20 > 10, then 20 × 2 > 10 × 2

If x < y, and z < 0 then x × z > y × z

Example: Suppose 2 < 5, then 2 × -4 > 5 × -4 ( -8 > -20. z = -4 and -4 < 0 )

If x > y, and z < 0 then x × z < y × z

Example: Suppose 5 > 1, then 5 × -2 < 1 × -2 ( -10 < -2 )



Division property:

It works exactly the same way as multiplication

If x < y, and z > 0 then x ÷ z < y ÷ z

Example: Suppose 2 < 4, then 2 ÷ 2 < 4 ÷ 2

If x > y, and z > 0 then x ÷ z > y ÷ z

Example: Suppose 20 > 10, then 20 ÷ 5 > 10 ÷ 5

If x < y, and z < 0 then x ÷ z > y ÷ z

Example: Suppose 4 < 8, then 4 ÷ -2 > 8 ÷ -2 ( -2 > -4 )

If x > y, and z < 0 then x ÷ z < y ÷ z

Example: Suppose 5 > 1, then 5 ÷ -1 < 1 ÷ -1 ( -5 < -1 )

Transitive property:

If x > y and y > z, then x > z

Example: Suppose 10 > 5 and 5 > 2, then 10 > 2

x < y and y < z, then x < z

5 < 10 and 10 < 20, then 5 < 20

Comparison property:

If x = y + z and z > 0 then x > y

Example: 6 = 4 + 2, then 6 > 4

The properties of inequality are more complicated to understand than the property of equality.

Allow yourself plenty of time as you go over this lesson.Any questions about the properties of inequality, let me know.





Recent Articles

  1. Conjugate in Algebra

    Oct 16, 17 09:34 AM

    What is the conjugate in algebra? A concise and clear explanation.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape





Recent Lessons

  1. Conjugate in Algebra

    Oct 16, 17 09:34 AM

    What is the conjugate in algebra? A concise and clear explanation.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

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


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz