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
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