Name _______________________________________ Date __________________ Class __________________
LESSON
6-3
Inequalities
NOTES
An equation is a statement that says two quantities are equal. An inequality is a
statement that says two quantities are not equal. The chart shows symbols and
phrases that indicate inequalities.
<
Less than
Fewer than
Below


Less than or equal to
At most
No more than
Greater than or equal to
At least
No less than
>
Greater than
More than
Above
Complete the inequality for each situation.
1. No more than 200 people can be seated in the restaurant.
p = number of people seated in restaurant
p _____ 200
2. The waiting time for a table is at least 20 minutes.
w = waiting time
w _____ 20 minutes
3. The price of all special dinner entrees is below $10.
d = special dinner entrees
d _____ $10
4. The Yoshida family spent more than $40 for dinner.
y = Yoshida family spent
y _____ $40
An inequality can be shown on a graph.
The graph shows:
Inequality
All numbers greater
than 3
x>3
All numbers greater
than or equal to 3
x≥3
All numbers less
than 3
x< 3
All numbers less
than or equal to 3
x≤ 3
Graph
The open circle at 3 shows that the
value 3 is not included in the graph.
The closed circle at 3 shows that
the value 3 is included in the graph.
Name _______________________________________ Date __________________ Class __________________
LESSON
6-3
Inequalities (continued)
NOTES
Graph each inequality.
5. x > 4
6. x  1
• Draw an open circle at 4.
• Draw a closed circle at 1.
• Read x > 4 as “x is greater
than 4.”
• Read x  1 as “x is
less than or equal to 1.”
• Draw an arrow to the right of 4.
• Draw an arrow to the left of 1.
7. a > 1
8. y  3
A compound inequality is a combination of two inequalities.
The graph shows:
Inequality
All numbers from 2 to 2
2  x  2
All numbers greater than 2
or less than 2
Graph
x > 2 or x < 2
Graph each compound inequality.
9. 0 < x  3
10. x  4 or x  1
• Draw an open circle at 0 and a
closed circle at 3.
• Draw a closed circle at 1 and
a closed circle at 4.
• Shade the line between 0 and 3.
• Shade the line to the left of 1 and
to the right of 4.