1. Preview
Warm Up
California Standards
Lesson Presentation

2. 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

3. AF4.0 Students solve simple linear equations and inequalities over the rational numbers.
Also covered: AF1.1
California
Standards

4. 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.

5. 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!

6. Solve and graph. a 4 12 < a 4 4 • 12 < 4 •
Multiply both sides by 4.
48 < a, or a > 48

7. 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.

8. Solve and graph.
–9b ≤ 45 ≥
45 –9
– 9b –9
Divide both sides by –9; ≤ changes to ≥
BECAUSE WE DIVIDED BY A NEGATIVE.
b ≥ –5 –5

9. Solve and graph. b 5 16 > b 5 Multiply both sides by 5.
5 • 16 > 5 •
b 5
Multiply both sides by 5.
80 > b, or b < 80

10. Check
According to the graph, 79 should be a solution and 81 should not be a solution.
16 >
b 5
16 >
b 5
Substitute 79 for b.
Substitute 81 for b.
16 >
79 5 ?
16 >
81 5 ?
16 > 15.8 ?
16 > 16.2 ? x
So 79 is a solution.
So 81 is not a solution.

11. Solve and graph.
12 ≤ –4a ≥
–4a –4 –4
Divide both sides by –4; ≤ changes to ≥
BECAUSE WE DIVIDED BY A NEGATIVE.
–3 ≥ a –3

12. –2 1. –14x > 28 2 x < –2 x 3 2. < 15 50 40 45 x < 45
Lesson Quiz: 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 Quiz: 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