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### Writing Inequalities

• A mathematical sentence that contains one of the following symbols is an inequality.
•  Verbal Description Symbol Is less than < Is greater than > Is less than or equal to ≤ Is greater than or equal to ≥ Is not equal to ≠
• The solution of an inequality is any value that makes the inequality true. The graph of an inequality shows that an inequality can have many solutions. A closed circles indicates that a value is included. An open circle indicates that a value is not included.

### Writing Inequalities

Write an inequality for the verbal description, The price p is more than \$ 3. Graph the description on a number line.
p > 3
Write an inequality for the verbal description, A wage w is at least \$ 9.30. Graph the description on a number line.
w ≥ 9.30
During a recent storm, the wind speed was greater than 44 mph but less than 56 mph. Write an inequality to represent this situation and graph using a number line.
• s > 44, s < 56
44 < s < 56
A price of a room at a motel is at least \$ 40.00 and at most \$ 125.00. Write an inequality and graph.
• p ≥ 40, p ≤ 125
40 ≤ p ≤ 125
To meet a company's standards of quality, the weight of a burrito has to be within 0.5 ounces of the weight listed on the packaging. The burrito is listed as 8.5 ounces. Write an inequality describing the permissible weights of the burrito and graph.
8 ≤ b ≤ 9
You need to have taken at least 10.5 units of introductory psychology courses before you can become a psychology major. Write an inequality representing the situation. Can Lillian, who has taken 3 introductory courses at 3 units each, declare her psychology major?
• u ≤ 10.5
• Lillian has taken 9 total units: 9 < 10.5
u ≤ 10.5
No
Write an inequality for the verbal description, A number x is not negative. Graph the inequality.
x ≥ 0
Write a system of inequalities for this situation: The temperature should be less than 90° F but at least 75° F. Graph the solution.
75° F ≤ t < 90° F
Write an inequality for 4 is at least half of a number.
• ät least" means " ≥ "
• ä number" is represented by "x"
4 ≥ [1/2]x
Write and use an inequality to solve the problem. A child must be at least 4 feet 11 inches to not need a child seat in a vehicle. Use the table to identify the children that need a child seat.
 Child Height Eric 5'11" Michelle 4'10" Duy 4'11" Tiffany 4'5" David 3'11"
• h ≥ 4 ft 11 in
Michelle, Tiffany, and David need child seats

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Writing Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:15
• Inequality
• System of Inequalities
• Solution of an Inequality
• Writing an Inequality 2:10
• Example: Price p is More than \$6
• Writing an Inequality 3:53
• Example: Wage w is at Least \$8.25
• Writing a System of Inequalities 5:24
• Example: System of Inequalities for Wind Speed
• Writing a System of Inequalities 9:03
• Example: Price of a Room in Las Vegas
• Identifying Solutions of an Inequality 10:33
• Example: Driver's Permit
• Extra Example 1: Writing Inequalities 12:03
• Extra Example 2: Writing a System of Inequalities 13:24
• Extra Example 3: Writing Inequalities 14:51
• Extra Example 4: Using Inequality to Solve Word Problem 15:31