1. Introduction to Inequalities
1-9
Introduction to Inequalities
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Warm Up
Solve.
1. x + 6 = 13
2. 8n = 48
3. t  2 = 56
4. 6 =
x = 7
n = 6
t = 58 z 6
z = 36

3. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Problem of the Day
Bill and Brad are taking Drivers education class. Bill drives with his instructor for one and a half hours three times a week. He needs a total of 27 hours. Brad drives two times a week, two hours each time. He needs 26 hours. Who will finish his hours first?
Bill

4. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Learn to solve and graph inequalities.

5. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Vocabulary
inequality
algebraic inequality
solution set

6. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
An inequality compares two quantities and typically uses one of these symbols: 
<
is less than
is greater than  
is less than or equal to
is greater than or equal to

7. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Additional Example 1: Completing an Inequality
Compare. Write < or >.
A. 23 –
>
B. 5(12)
<

8. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Check It Out: Example 1
Compare. Write < or >.
A. 19 –
<
B. 4(15)
>

9. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
An inequality that contains a variable is an algebraic inequality.
A number that makes an inequality true is a solution of the inequality.
The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.

10. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
An open circle means that the corresponding value is not a solution. A solid circle means that the value is part of the solution set.
Helpful Hint!

11. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Word Phrase
Inequality
Sample Solutions
Solution Set
x is less than 5
x < 5
x = 4
4 < 5
x = 2.1
2.1 < 5

12. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Word Phrase
Inequality
Sample Solutions
Solution Set
a is greater than 0
a is more than 0
a > 0
a = 7
7 > 0
a = 25
25 > 0
–3 –2 –

13. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Word Phrase
Inequality
Sample Solutions
Solution Set
y is less than or equal to 2
y is at most 2
y  2
y = 0
0  2
y = 1.5
1.5  2
–3 –2 –

14. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Word Phrase
Inequality
Sample Solutions
Solution Set
m is greater than or equal to 3
m is at least 3
m  3
m = 17
17  3
m = 3
3  3 –

15. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Most inequalities can be solved the same way equations are solved.
Use inverse operations on both sides of the inequality to isolate the variable.
There are special rules when multiplying or dividing by a negative number, which you will learn in the next chapter.

16. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
The inequality symbol opens to the side with the greater number.
2 < 10
Remember!

17. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Additional Example 2A: Solving and Graphing Inequalities
Solve and graph the inequality.
x  8
–2.5
–2.5
Subtract 2.5 from both sides.
x  5.5
According to the graph, 5.4 is a solution, since 5.4 < 5.5, and 6 should not be solution because 6 > 5.5.

18. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Additional Example 2A Continued
Solve and graph the inequality.
Check
x < 8 ?
< 8 ?
Substitute 5.4 for x.
7.9< 8 ? 
So 5.4 is a solution.
Check
x < 8 ?
< 8 ?
Substitute 6 for x.
8.5< 8 ? 
So 6 is not a solution.

19. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Additional Example 2B: Solving and Graphing Inequalities
Solve and graph the inequality.
w – 1 < 8
Add 1 to both sides.
w < 9 –

20. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Check It Out: Example 2
Solve and graph each inequality.
A. x + 2  3.5 –2 –2
Subtract 2 from both sides.
x  1.5
B. 6u > 72
6u > 72
Divide both sides by 6. 6 6
u > 12

21. Introduction to Inequalities
1-9
Introduction to Inequalities
Course 3
Lesson Quiz
Use < or > to compare each inequality.
(2) –
Solve and graph each inequality.
3. k + 9 < 12
4. 3 
5. A school bus can hold 64 passengers. Three classes would like to use the bus for a field trip. Each class has 21 students. Write and solve an inequality to determine whether all three classes will fit on the bus.
>
>
k< 3
–5 –4–3–2– m 2
6  m
–4 –3–2–
3(21)  64; 63  64; yes ?