11-4 Inequalities
Learn to read and write inequalities and
graph them on a number line.
Course 2
11-4 Inequalities
Insert Lesson Title Here
Vocabulary
inequality
algebraic inequality
solution set
compound inequality
Course 2
1. Write down the problem: Variable Side
Answer Side
2. Isolate the variable by doing the inverse operation on both
sides- starting with the variable side.
3. Cross out on variable side
4. Draw answer line
5. Drop down the variable
6. Solve – find a solution
7. Check
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
<
>
Course 2
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
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.
B. The tram attendant will allow no more
than 60 people on the tram.
number of people ≥ 15
number of people ≤ 60
Course 2
“No more than” means
less than or equal to.
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.
gallons of gas ≤ 10
“At most” means less
than or equal to.
B. There is at least 10 yards of fabric left.
yards of fabric ≥ 10
Course 2
“At least” means
greater than or equal to.
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.
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
Course 2
11-4 Inequalities
Additional Example 2A & 2B: Graphing Simple
Inequalities
Graph each inequality.
A. n < 3
–3
–2
–1
0
1
2
3
B. a ≥ –4
–6
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–4
–2
0
2
4
6
3 is not a solution, so
draw an open circle at
3. Shade the line to
the left of 3.
–4 is a solution, so
draw a closed circle
at –4. Shade the line
to the right of –4.
11-4 Inequalities
Try This: Example 2A & 2B
Graph each inequality.
A. p ≤ 2
–3
–2
–1
0
1
2
3
B. e > –2
–3
Course 2
–2
–1
0
1
2
3
2 is a solution, so
draw a closed circle at
2. Shade the line to
the left of 2.
–2 is not a solution, so
draw an open circle
at –2. Shade the line
to the right of –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 4.
y is between –2 and 4.
Writing Math
The compound inequality –2 < y and y < 4
can be written as –2 < y < 4.
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
•
–6 – 4 – 2
0
2 4
–6 –4 –2
6
0
º
2
4
6
Then combine the graphs.
–6 –5 –4 –3 –2 – 1
0
1
2
3
4 5
6
The solutions of m ≤ –2 or m > 1 are the combined
solutions of m ≤ –2 or m > 1.
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
º
–6 –4 –2
0
2
4
6
– 6 –4 – 2
•
0
2
4
6
Then combine the graphs. Remember that
–3 < b ≤ 0 means that b is between –3 and 0, and
includes 0.
–6 –5 –4 –3 –2 – 1
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0
1
2
3
4 5
6
11-4 Inequalities
Try This: Example 3A
Graph each compound inequality.
A. w < 2 or w ≥ 4
First graph each inequality separately.
w<2
–6 – 4 – 2
0
2 4
W≥4
–6 –4 –2
6
0
2
4
6
Then combine the graphs.
–6 –5 –4 –3 –2 – 1
0
1
2
3
4 5
6
The solutions of w < 2 or w ≥ 4 are the combined
solutions of w < 2 or w ≥ 4.
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
–6 –4 –2
0
2
4
º
•
6
– 6 –4 – 2
0
2
4
6
Then combine the graphs. Remember that
5 > g ≥ –3 means that g is between 5 and –3, and
includes –3.
–6 –5 –4 –3 –2 – 1
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0
1
2
3
4 5
6
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.
people in the theater ≤ 220
2. There are at least a dozen eggs left.
number of eggs ≥ 12
3. Fewer than 14 people attended the meeting.
people attending the meeting < 14
Course 2
11-4 Inequalities
Insert Lesson Title Here
Lesson Quiz: Part 2
Graph the inequalities.
4. x > –1
º
–3 –2 –1
0
1 3
5
5. x ≥ 4 or x < –1
º
–5 –3 –1
Course 2
•
0
1 3
5