1. 1. Is –9 a solution of a + 7 = –2?
ANSWER
yes
2. Solve the equation h + 12 = –8.
ANSWER
–20

2. 3. Write an inequality that describes the number of CDs you can buy for $12 each if you have no more than $60 to spend. Can you buy 6 CDs?
ANSWER
12x ≤ 60; no

3. EXAMPLE 1
Write and graph an inequality
Death Valley
The highest temperature recorded in the United States was 134°F at Death Valley, California, in Use only this fact to write and graph an inequality that describes the temperatures in the United States.
SOLUTION
Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134.

4. EXAMPLE 2
Write inequalities from graphs
Write an inequality represented by the graph. a.
SOLUTION a.
The open circle means that –6.5 is not a solution of the inequality. Because the arrow points to the right, all numbers greater than –6.5 are solutions.
ANSWER
An inequality represented by the graph is x > –6.5.

5. EXAMPLE 2
Write inequalities from graphs b.
SOLUTION b.
The closed circle means that 4 is a solution of the inequality. Because the arrow points to the left, all numbers less than 4 are solutions.
ANSWER
An inequality represented by the graph is x ≤ 4.

6. GUIDED PRACTICE
for Example 1 and 2
Write an inequality represented by the graph.
ANSWER
x ≥ –2.5

7. Solve an inequality using addition
EXAMPLE 3
Solve an inequality using addition
x – 5 > –3.5. Graph your solution.
Solve
x – 5 > –3.5
Write original inequality.
x – > –
Add 5 to each side.
x > 1.5
Simplify.
ANSWER
The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for x in the original inequality.

8. Solve an inequality using addition
EXAMPLE 3
Solve an inequality using addition
CHECK
x – 5 > –3.5
Write original inequality.
6 – 5 > –3.5 ?
Substitute 6 for x.
1 > –3.5
Solution checks.

9. GUIDED PRACTICE
for Example 3
Solve the inequality. Graph your solution.
4. x – 9 ≤ 3
x ≤ 12
ANSWER

10. GUIDED PRACTICE
for Example 3
Solve the inequality. Graph your solution.
5. p – 9.2 < –5
p < 4.2
ANSWER

11. GUIDED PRACTICE
for Example 3
Solve the inequality. Graph your solution.
6. –1 ≥ m – 1 2
m ≤ 1 2 –
ANSWER

12. EXAMPLE 5
Solve a real-world problem
LUGGAGE WEIGHTS
You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weights w (in pounds) that you can add to the bag.
SOLUTION
Write a verbal model. Then write and solve an inequality.
w ≤

13. Solve a real-world problem
EXAMPLE 5
Solve a real-world problem
w ≤ 50
Write inequality.
w – 16.8 ≤ 50 – 16.8
Subtract 16.8 from each side.
w ≤ 33.2
Simplify.
ANSWER
You can add no more than 33.2 pounds.

14. GUIDED PRACTICE
for Examples 4 and 5
7. Solve y > 6. Graph your solution.
y > 0.5
ANSWER

15. GUIDED PRACTICE
for Examples 4 and 5
8. WHAT IF? In Example 5, suppose your bag weighs 29.1 pounds. Find the possible weights (in pounds) that you can add to the bag.
w ≤ 20.9 lb
ANSWER

16. Warm-up: Page 296 #1-19 all Homework: Page 301 #3-28 all

17. Example 1
Antarctica
The lowest temperature recorded in Antarctica was –129°F at the Russian Vostok station in Use only this fact to write and graph an inequality that describes the temperatures in Antarctica.
ANSWER
x ≥ –129°F

18. GUIDED PRACTICE
Write an inequality represented by the graph.
ANSWER
x < 8

19. Daily Homework Quiz
Solve the inequality. Graph your solution.
3. s ≥ –1.5
ANSWER
all real numbers greater than or equal to –2
k – 6 < –5 4.
ANSWER
all real numbers less than 1

20. Solve an inequality using subtraction
EXAMPLE 5
Solve an inequality using subtraction
Solve 9 ≥ x + 7. Graph your solution.
9 ≥ x + 7
Write original inequality.
9 – 7 ≥ x + 7 – 7
Subtract 7 from each side.
2 ≥ x
Simplify.
ANSWER
You can rewrite 2 ≥ x as x ≤ 2. The solutions are all real numbers less than or equal to 2.

21. Daily Homework Quiz
A theater can seat at most 625 people. The box office has sold tickets for 284 seats. Write and solve an inequality to find the possible numbers of remaining tickets t the box office can sell. 6.
ANSWER
t ≤ 625; t ≤ 341; no more than 341 tickets.