6.04 Identify and write inequalities
Introduction
So far we have learned about equations, a statement where one side is equal to to the other side. There will be times when we want to compare two quantities where one is smaller or larger than the other.
An inequality exists when one amount is not equal to the other. We can think of this as a set of unbalanced scales, where one side is heavier than the other.
Identify and write inequalities
In mathematics we have special symbols to indicate that an inequality exists. Let's review them now.
- >: the greater than symbol.
- <: the less than symbol.
- \geq: the greater than or equal to symbol.
- \leq: the less than of equal to symbol.
When we write an equation, we are able to write it in two orders. For example, x=10 and 10=x mean the same thing.
We can also write inequality statements in two orders, but we need to be careful and switch the inequality sign being used as well. For example, x>10 means the same thing as 10<x. That is, "x is greater than ten" is the same as "ten is less than x".
Examples
Example 1
Write a mathematical statement to mean "k is less than or equal to seven."
Example 2
Write a mathematical statement to mean "The sum of 5 groups of x, and 3 is at least 23. "
The smaller side of the inequality symbol matches the side with the smaller number. That is, the inequality symbol "points to" the smaller number.
The greater than symbol is >.
The less than symbol is <.
The greater than or equal to symbol is \geq.
The less than or equal to symbol is \leq.