  ## Math Properties . . . Reversal Property of Inequality

Math Properties - Reversal -

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"

The Reversal Property of Inequality states that an inequality (the entire expression) can be reversed without affecting the validity of the expression.

When an inequality sign is reversed, the expressions and the right and left hand side of the inequality sign trade places. The expression on the right is placed on the left hand side of the inequality symbol, and the expression on the left is placed on the right hand side of the inequality symbol.

Examples follow.

a = any real number, b = any real number

If a b, then b a

If a b, then b a

If a b, then b a

If a b, then b a

If 5 1, then 1 5

If x + 3 y, then y x + 3

If Jim weighs more than Frank, then Frank weighs less than Jim.