1. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Learn to solve and graph inequalities.

2. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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

3. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Example 1: Completing an Inequality
Compare. Write < or >.
A. 23 –
>
B. 5(12)
<

4. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Word Phrase
Inequality
Sample Solutions
Solution Set
x is less than 5
x < 5
x = 4
4 < 5
x = 2.1
2.1 < 5

5. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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 –

6. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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 –

7. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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 –

8. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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.

9. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Example 2A: Solving and Graphing Inequalities
Solve and graph the inequality.
A. 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.

10. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Example 2B: Solving and Graphing Inequalities
Solve and graph the inequality.
B. 5t > 15
5t > 15
Divide both sides by 5. 5 5
t > 3

11. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Example 2C: Solving and Graphing Inequalities
Solve and graph the inequality.
C. w – 1 < 8
Add 1 to both sides.
w < 9 –

12. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Example 2D: Solving and Graphing Inequalities
Solve and graph the inequality. p 4
D. 3 ≥
3 ≥ p 4
4 •
4 •
Multiply both sides by 4.
12 ≥ p

13. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
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

14. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Examples 2A and 2B
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

15. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Examples 2C and 2D
Solve and graph each inequality.
C. z – 6 < 15
Add 6 to both sides.
z < 21
–21 –14 –
D. 2 ≥ b 9
2 ≥ b 9
9 •
9 •
Multiply both sides by 9.
18 ≥ b

16. Solving Simple Inequalities 1-5 Solving Simple Inequalities
Pre-Algebra
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Example 3
Mr. Minturn will provide 130 cookies for the 7th grade. He has to buy the cookies in packages of 20. What is the least number of packages Mr. Minturn must buy to be sure to have enough cookies?

17. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Example 3
Understand the Problem
The answer will be the number of packages of cookies a customer needs to purchase.
List the important information:
Cookies are sold in packages of 20 cookies.
A customer needs to purchase 130 cookies.
Show the relationship of the information:
the number of packages of cookies to be purchased
the number of cookies in one package
130 cookies • ≥

18. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Example 3 Continued 2
Make a Plan
Use the relationship to write an inequality. Let x represent the number of packages of cookies. x •
20 cookies ≥
130 cookies

19. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Example 3 Continued
Solve 3
20x ≥ 130
20x ≥ 130
Divide both sides by 20. 20 20
x ≥ 6.5
At least 6.5 packages of cookies need to be purchased.

20. Solving Simple Inequalities
1-5
Solving Simple Inequalities
Pre-Algebra
Try This: Example 3 Continued 4
Look Back
Because whole packages of cookies must be purchased, at least 7 packages of cookies must be purchased for the party.