1.
SECTION 3-6
Graphing Inequalities on a Number Line
2.
ESSENTIAL QUESTIONS
How do you determine if a number is a solution of an
inequality?
How do you graph the solution of an inequality on a
number line?
Where you’ll see this:
Business, government, sports, physics, geography
3.
VOCABULARY
1. Inequality:
2. True Inequality:
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:
4.
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality:
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:
5.
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisﬁes the
conditions
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:
6.
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisﬁes the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality:
5. Solution of the Inequality:
7.
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisﬁes the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality: When there is a variable in the inequality
5. Solution of the Inequality:
8.
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisﬁes the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality: When there is a variable in the inequality
5. Solution of the Inequality: Find all values that make the
inequality true
11.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
Less than Maximum Minimum
12.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥
Less than Maximum Minimum
13.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤
Less than Maximum Minimum
14.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
15.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
<
16.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
< ≤
17.
SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
< ≤ ≥
18.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
19.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
20.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
21.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
22.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No
23.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No Yes
24.
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No Yes No
25.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
26.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6
27.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6
28.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6
29.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6
30.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6
31.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
32.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
33.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
34.
EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
35.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
b. Graph the solution of the inequality on a number line.
36.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
b. Graph the solution of the inequality on a number line.
37.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
38.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250
39.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250
40.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250
41.
EXAMPLE 3
By order of the ﬁre commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250
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