Slide 1ANSWER
Solve the inequality.
You estimate you can read at least 8 history text
pages per day. What are the possible numbers of
day it will take you to read at most 118 pages?
6.4
graph the inequality.
a.
All real numbers that are greater than –2 and less
than 3
Graph:
b.
All real numbers that are less than 0 or greater than
or equal to 2
Translate the verbal phrase into an inequality. Then
graph the inequality.
To –3 and less than 5
All real numbers that are less than –1 or greater than
or equal to 4
Example 2
CAMERA CARS
A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane.
6.4
Example 2
Let h represent the height (in feet) of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4 h 18.
SOLUTION
6.4
Investing
An investor buys shares of a stock and will sell them if the change c in value from the purchase price of a share is less than –$3.00 or greater than $4.50. Write and graph a compound inequality that describes the changes in value for which the shares will be sold.
3.
ANSWER
6.4
Separate the compound inequality into two inequalities. Then solve each inequality separately.
Write two inequalities.
Simplify.
The compound inequality can be written as –3 < x < 4.
2 < x + 5
x + 5 < 9
and
The solutions are all real numbers greater than –3 and
less than 4.
–7 < x – 5 < 4
10 2y + 4 24
Graph:
3
Multiply each expression by –1 and reverse both inequality symbols.
Simplify.
–5 –x – 3 2
Add 3 to each expression.
–2 –x 5
2 x –5
–5 x 2
ANSWER
The solutions are all real numbers greater than or equal to –5 and less than or equal to 2.
6.4
7. –14 < x – 8 < –1
8. –1 –5t + 2 4
–6 < x < 7
inequality.
SOLUTION
Solve 2x + 3 < 9 or 3x – 6 > 12. Graph your solution.
Solve the two inequalities separately.
Addition or
or
2x < 6
ANSWER
The solutions are all real numbers less than 3 or greater
than 6.
9. 3h + 1< – 5
ANSWER
ANSWER
6.4
Astronomy
• Identify three possible temperatures (in degrees Fahrenheit) at a landing site.
• Solve the inequality. Then graph your solution.
• Write a compound inequality that describes the possible temperatures (in degrees Fahrenheit) at a landing site.
The Mars Exploration Rovers Opportunity and Spirit are robots that were sent to Mars in 2003 in order to gather geological data about the planet. The temperature at the landing sites of the robots can range from 100°C to 0°C.
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SOLUTION
Write a compound inequality. Because the temperature at a landing site ranges from –100°C to 0°C, the lowest possible temperature is –100°C, and the highest possible temperature is 0°C.
–100 C 0
9
5
5
9
C = (F – 32).
Let F represent the temperature in degrees Fahrenheit, and let C represent the temperature in degrees
Celsius. Use the formula
Write inequality from Step 1.
–148 F 32
5
9
Identify three possible temperatures.
The temperature at a landing site is greater than or equal to –148°F and less than or equal to 32°F. Three possible temperatures are –115°F, 15°F, and 32°F.
6.4
Guided Practice
• Write and solve a compound inequality that describes the possible temperatures (in degree Fahrenheit) on Mars.
• Graph your solution. Then identify three possible temperatures (in degrees Fahrenheit) on Mars.
Mars has a maximum temperature of 27°C at the equator and a minimum temperature of –133°C
at the winter pole.
ANSWER
ANSWER
6.4
Lesson Quiz
1. Solve x + 4 < 7 or 2x – 5 > 3. Graph your solution.
2.
Solve 3x + 2 > –7 and 4x – 1 < –5. Graph your solution.
ANSWER
all real numbers less than 3 or greater than 4
ANSWER
all real numbers greater than –3 and less than –1
6.4
Lesson Quiz
The smallest praying mantis is 0.4 inch in length. The largest is 6 inches. Write and graph a compound inequality that describes the possible lengths L of a praying mantis.
3.
ANSWER