1. Warm Up
Solve.
1. 2x + 8 = x – 7
2. –4(x + 3) = –5x – 2
3. 5x + x + (–11) = 25 – 3x
4. 6n + 9 – 4n = 3n
x = –15
x = 10
x = 4
n = 9

2. When you multiply (or divide) both sides of an inequality by a negative number, you must reverse the inequality symbol to make the statement true.

3. When graphing an inequality on a number line, an open circle means that the point is not part of the solution and a closed circle means that the point is part of the solution.
Remember!

4. Additional Example 1A: Solving Inequalities by Multiplying or Dividing
Solve and graph.
a 4
12 <
4 • 12 < 4 •
a 4
Multiply both sides by 4.
48 < a, or a > 48

5. Additional Example 1A Continued
Check
According to the graph, 49 should be a solution and 47 should not be a solution.
12 <
a 4
12 <
a 4
Substitute 49 for a.
Substitute 47 for a.
12 <
49 4 ?
12 <
47 4 ?
12 < 12.25 ?
12 < 11.75 ? x
So 49 is a solution.
So 47 is not a solution.

6. Additional Example 1B: Solving Inequalities by Multiplying or Dividing
Solve and graph.
–9b ≤ 45 ≥
45 –9
– 9b –9
Divide both sides by –9; ≤ changes to ≥.
b ≥ –5 –5

7. Additional Example 2: Problem Solving Application
A rock-collecting club needs to make at least $500. They are buying rocks for $2.50 and selling them for $4.00. What is the least number of rocks the club must sell to make the goal?

8. Understand the Problem
Additional Example 2 Continued 1
Understand the Problem
The answer is the least number of rocks the club must sell to make their goal.
List the important information:
• The club needs to make at least $500.
• The club is buying rocks for $2.50.
• The club is selling rocks for $4.00.
Show the relationship of the information:
rocks sold $
rocks bought $
$500 - •
# of rocks ≥

9. Additional Example 2 Continued
Make a Plan
Use the information to write an inequality. Let r represent the number of rocks.
4.00
2.50
$500 - • r ≥

10. Additional Example 2 Continued
Solve 3
(4.00 – 2.50) • r ≥ 500
1.50r ≥ 500
Simplify.
1.50r ≥ 500
Divide both sides by 1.50.
r ≥ …
334 rocks need to be sold in order for the club to make at least $500.

11. Additional Example 2 Continued4
Look Back
Since the rock-collecting club is reselling rocks, they are making a $1.50 profit from each rock. $1.50(334) ≥ $500, or $501 ≥ $500.

12. –2 1. –14x > 28 2 x < –2 x 3 2. < 15 50 40 45 x < 45
Lesson Review: Part I
Solve and graph.
1. –14x > 28 –2 2
x < –2 x 3
< 15 50 40 45
x < 45
3. 18 < –6x
–3 > x q 8 4.
 5
q ≥ 40 40 45

13. Lesson Review: Part II 5.
Jared isn’t supposed to carry more than 35 pounds in his backpack. He has 8 textbooks and each book weighs 5 pounds. What is the greatest amount of textbooks he can carry in his backpack at one time?
No more than 7