2. What is an inequality?
• Mathematical sentence that compares
quantities.
• To solve an inequality you have to find values
for the variable that make the sentence true.
• Inequalities do not contain equal signs.
3. Inequality symbols
Symbols < > ≤ ≥ ≠
Words • less
than
• fewer
than
• smaller
than
• below
• greater
than
• more than
• Exceeds
• larger than
• above
• less than or
equal to
• no more
than
• at most
• Maximum
• not greater
than
• greater than
or equal to
• no less than
• at least
• Minimum
• Not smaller
than
• does
not
equal
4. Translating sentences to
inequalities
• TIPS
– Use a variable to represent the unknown
– Look for key words to determine the inequality
symbol you will use.
• Example 1:
A numberis greater than 2.
We don’t know
what the number
is. We will use x to
represent the
unknown number.
x > 2
5. More Examples
• Example 2:
• Example 3:
The maximum is 28.
value of a number
We don’t know what the
number is. We will use x to
represent the number.
x ≤ 28
A number isgreater than or equal to four.
We don’t know what the
number is. We will use x to
represent the number.
x ≥ 4
6. Graphing inequalities
• Steps:
– Draw a number line and place the number in the problem
in the middle of the number line.
– Fill in numbers on the number line.
– Put a circle on the number 2 on the number line.
• For this example, you leave the circle open (not colored
in).
– Shade in the part of the number line that shows the
numbers that are greater than 2.
• Example 1:
x > 2 0 1 2 3 4
7. Examples with Graphing
Inequalities
Example 2:
x ≤ 28
Example 3:
x ≥ 4
-Both of these examples mean that the variable can be equal
to the number in the inequality.
-When you graph these inequalities, color in the circle.
