1. Warm Up Lesson Presentation Lesson Quiz
Solve Inequalities Using Addition and Subtraction
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
1. Is –9 a solution of a + 7 = –2?
ANSWER
yes
2. Solve the equation h + 12 = –8.
ANSWER
–20
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
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. Guided Practice
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 the Antarctica.
ANSWER
x  –129F

5. Example 2
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.

6. Example 2 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.

7. Guided Practice
Write an inequality represented by the graph.
ANSWER
x < 8
ANSWER
x  –2.5

8. x – 5 > –3.5. Graph your solution. Solve
Example 3
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.

9. Example 3 CHECK x – 5 > –3.5 6 – 5 > –3.5 1 > –3.5
Write original inequality.
6 – 5 > –3.5 ?
Substitute 6 for x.
1 > –3.5
Solution checks.

10. Guided Practice
Solve the inequality. Graph your solution.
4. x – 9  3
x  12
ANSWER
5. p – 9.2 < –5
p < 4.2
ANSWER
6. –1  m – 1 2
m  1 2 –
ANSWER

11. Solve 9  x + 7. Graph your solution.
Example 4
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.

12. Guided Practice
7. Solve y > 6. Graph your solution.
y > 0.5
ANSWER

13. Example 5
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 

14. You can add no more than 33.2 pounds.
Example 5
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.

15. Guided Practice
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. Lesson Quiz
Solve the inequality. Graph your solution.
1. s  –1.5
ANSWER
all real numbers greater than or equal to –2
k – 6 < –5 2.
ANSWER
all real numbers less than 1

17. Lesson 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. 3.
ANSWER
t  625; t  341; no more than 341 tickets.