Simple Inequalities
General Explanation
An INEQUALITY is a statement which shows that two quantities are not equal.
If two quantities are not equal, then one is greater than the other.
The symbol for equality is "=". The symbols for inequality are: ">" for "greater than" "<" for "less than"The following expression states that x is greater than 6: x > 6The following states that x is greater than or equal to 6: x ≥ 6Similarly, the following states that x is less than or equal to 6: x ≤ 6On the number line, x > 6 represents all the numbers to the right of 6, while x ≥ 6 means 6 and all the numbers to the right of 6. Similarly, x < 6 represents all the numbers to the left of 6, while x ≤ 6 represents 6 and all the numbers to the left of 6. Sample Problem 1
Write an inequality to represent the numbers shown by the red arrow in the following graph:
Solution
The arrow contains points to the right of the number 5, but it does not include 5 because there is an open circle
over the number. So the arrow represents all the numbers greater than 5.
This can be represented by the following inequality: x > 5 Sample Problem 2
Draw a graph for the inequality:
x ≤ 3 Solution
We see that the inequality contains a "less than or equal to" sign, so we know the graph
will include the point 3. We fill in a circle at this point:
Since x is LESS than or equal to 3, we draw the arrow to the left:
The red arrow represents the inequality x ≤ 3.
