1. 11-4
Inequalities
Course 2

2. Course 2
11-4
Inequalities
Learn to read and write inequalities and graph them on a number line.

3. Insert Lesson Title Here
Course 2
11-4
Inequalities
Insert Lesson Title Here
Vocabulary
inequality
algebraic inequality
solution set
compound inequality

4. Inequalities 11-4 An inequality states that two quantities
Course 2
11-4
Inequalities
An inequality states that two quantities
either are not equal or may not be
equal. An inequality uses one of the
following symbols:
Symbol
Meaning
Word Phrases
<
> ≤ ≥
is less than
Fewer than, below
is greater than
More than, above
is less than or equal to
At most, no more than
is greater than or equal to
At least, no less than

5. Additional Example 1: Writing Inequalities
Course 2
11-4
Inequalities
Additional Example 1: Writing Inequalities
Write an inequality for each situation.
A. There are at least 15 people in the waiting room.
“At least” means greater
than or equal to.
number of people ≥ 15
B. The tram attendant will allow no more
than 60 people on the tram.
“No more than” means
less than or equal to.
number of people ≤ 60

6. Inequalities 11-4 Try This: Example 1
Course 2
11-4
Inequalities
Try This: Example 1
Write an inequality for each situation.
A. There are at most 10 gallons of gas in the tank.
“At most” means less
than or equal to.
gallons of gas ≤ 10
B. There is at least 10 yards of fabric left.
“At least” means
greater than or equal to.
yards of fabric ≥ 10

7. Course 2
11-4
Inequalities
An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality.
An inequality may have more than one solution. Together, all of the solutions are called the solution set.
You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle.

8. Inequalities 11-4 a > 5 b ≤ 3
Course 2
11-4
Inequalities
This open circle shows that 5 is not a solution.
a > 5
If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle.
This closed circle shows that 3 is a solution.
b ≤ 3

9. Additional Example 2A & 2B: Graphing Simple Inequalities
Course 2
11-4
Inequalities
Additional Example 2A & 2B: Graphing Simple Inequalities
Graph each inequality.
A. n < 3
3 is not a solution, so
draw an open circle at 3. Shade the line to the left of 3.
–3 –2 –
B. a ≥ –4
–4 is a solution, so
draw a closed circle
at –4. Shade the line
to the right of –4.
–6 –4 –

10. Inequalities 11-4 Try This: Example 2A & 2B Graph each inequality.
Course 2
11-4
Inequalities
Try This: Example 2A & 2B
Graph each inequality.
A. p ≤ 2
2 is a solution, so
draw a closed circle at 2. Shade the line to the left of 2.
–3 –2 –
B. e > –2
–2 is not a solution, so
draw an open circle
at –2. Shade the line
to the right of –2.
–3 –2 –

11. Course 2
11-4
Inequalities
A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.
x > 3 or x < –1
–2 < y and y < 4
x is either greater than 3 or less than–1.
y is both greater than –2 and less than y is between –2 and 4.
The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.
Writing Math

12. Additional Example 3A: Graphing Compound Inequalities
Course 2
11-4
Inequalities
Additional Example 3A: Graphing Compound Inequalities
Graph each compound inequality.
A. m ≤ –2 or m > 1
First graph each inequality separately.
m ≤ –2
m > 1 • 2 4 6 – 2 4 6 –2 –4 –6
Then combine the graphs. 1 2 3 4 5 6 –
The solutions of m ≤ –2 or m > 1 are the combined solutions of m ≤ –2 or m > 1.

13. Additional Example 3B: Graphing Compound Inequalities
Course 2
11-4
Inequalities
Additional Example 3B: Graphing Compound Inequalities
Graph each compound inequality
B. –3 < b ≤ 0
–3 < b ≤ 0 can be written as the inequalities
–3 < b and b ≤ 0. Graph each inequality separately.
–3 < b
b ≤ 0 • 2 4 6 –2 –4 –6 2 4 6 –
Then combine the graphs. Remember that –3 < b ≤ 0 means that b is between –3 and 0, and includes 0. 1 2 3 4 5 6 –

14. Inequalities 11-4 Try This: Example 3A Graph each compound inequality.
Course 2
11-4
Inequalities
Try This: Example 3A
Graph each compound inequality.
A. w < 2 or w ≥ 4
First graph each inequality separately.
w < 2
W ≥ 4 2 4 6 – 2 4 6 –2 –4 –6
Then combine the graphs. 1 2 3 4 5 6 –
The solutions of w < 2 or w ≥ 4 are the combined solutions of w < 2 or w ≥ 4.

15. Inequalities 11-4 • º Try This: Example 3B
Course 2
11-4
Inequalities
Try This: Example 3B
Graph each compound inequality
B. 5 > g ≥ –3
5 > g ≥ –3 can be written as the inequalities
5 > g and g ≥ –3. Graph each inequality separately.
5 > g
g ≥ –3 • 2 4 6 –2 –4 –6 2 4 6 –
Then combine the graphs. Remember that > g ≥ –3 means that g is between 5 and –3, and includes –3. 1 2 3 4 5 6 –

16. Insert Lesson Title Here
Course 2
11-4
Inequalities
Insert Lesson Title Here
Lesson Quiz: Part 1
Write an inequality for each situation.
1. No more than 220 people are in the theater.
2. There are at least a dozen eggs left.
3. Fewer than 14 people attended the meeting.
people in the theater ≤ 220
number of eggs ≥ 12
people attending the meeting < 14

17. Insert Lesson Title Here
Course 2
11-4
Inequalities
Insert Lesson Title Here
Lesson Quiz: Part 2
Graph the inequalities.
4. x > –1 1 3 5 2 –
5. x ≥ 4 or x < –1 1 3 5 – •