1. Writing and Graphing Inequalities
Lesson 9.4

2. Vocabulary and Key Words
Inequality -a mathematical sentence that compares expressions. It contains the symbols <, >, ≤, or ≥.
A solution of an inequality is a value that makes the inequality true
solution set- the set of all solutions of an inequality
The graph of an inequality shows all of the solutions of the inequality on a number line

3. Is greater than or equal to
Key Symbols
Inequality Symbols
Symbol
<
>
Key Phrases
Is less than
Is fewer than
Is greater than
Is more than
Is less than or equal to
Is at most
Is no more than
Up to and including
Is greater than or equal to
Is at least
Is no less than
Note: To write an inequality, look for the above phrases to determine where to place the inequality symbol.

4. Example 1 Writing Inequalities
Write the word sentence as an inequality.
A number c is less than 4.
A number k plus 5 is greater than or equal to 8.
Four times a number q is at most 16.
A number t is no more than 7.
The difference of a number p and 3 is at least 10.
One-fourth of a number x is greater than 2.

5. Your Turn Write the word sentence as an inequality.
A number n is greater than 1.
Twice a number p is fewer than 7.
A number w minus 3 is less than or equal to 10.
A number z divided by 2 is at least 6.

6. Example 2 Checking Solutions

7. Example 2 Checking Solutions

8. Your Turn Tell whether 3 is a solution of the inequality. B + 4 < 6
18 ÷ x ≤ 10

9. Example 3 Graphing Inequalities
An open circle ○ is used when a number is not a solution. When the “or equal to/underline” is not there.
A closed circle ● is used when a number is a solution. When the “or equal to/underline” is there.
An arrow to the left or right shows that the graph continues in that direction.
Hint: If the variable comes first in the inequality, then the arrow points in the direction of the inequality.

10. Example 3 Graphing Inequalities
Graph the inequality
Graph g > 2.
Graph ½ ≥ h.

11. Your Turn
Graph the inequality.
4 > a
F ≤ 2.5
0 < n
P ≥ -3

12. Example 4
A classroom has enough room for up to 25 students. Write and graph an inequality that represents the number s of students in the classroom.

13. Your Turn Write and graph an inequality for the situation.
A cruise ship can carry at most 3500 passengers.
A board game is designed for ages 12 and up.

14. Assignment
Page 413 #17-38 all in Green Textbook