  ## Math Properties . . . Properties of Addition and Subtraction Applied to Inequalities

Math Properties - Inequalities: Addition & Subtraction -

Properties of Inequality :

In mathematics, inequalities compare numbers and expressions that are not equal to one another.

Generally, the following symbols are used for comparison: , , , .
Each of these symbols compares the relative size of two numbers to show which number is bigger, and which number is smaller.

Inequalities are important because they are common to everyday life experiences.

People intuitively use the concept of inequality to compare options and make choices based on relative value.

For example, a person may ask themselves: "Can I buy a new car with \$10,000 if a new car costs \$11,000?" The comparison of these choices is an inequality. One number is smaller than the other number.

Automatic control systems rely on this concept as well. A thermostat uses an inequality (comparing temperatures) to decide whether to turn on a heater or air conditioner. For example, the thermostat may turn on an air conditioner when the temperature rises above 85 degrees (or turn off the air conditioner when the temperature falls below 80 degrees).

The Properties of Inequality of Real Numbers - click description "Math Properties"   "Top of Page"

Property of Addition (and Subtraction) Applied to Inequalities

Properties of addition and subtraction apply to inequalities in the same way they apply to equalities. There are no differences.

Addition and Subtraction must be equally applied to both sides of the equation.

Examples follow.

a = any real number, b = any real number, c = any real number

If a b, then a + c b + c

If a b, then a - c b - c

If a b, then a + c b + c

If a b, then a - c b - c

If a b, then a + c b + c

If a b, then a - c b - c

If a b, then a + c b + c

If a b, then a - c b - c

If 10 1 , then 10 + 2 1 + 2

12 3

If 10 1, then 10 - 2 1 - 2

8 -1