Inequalities and Their Applications

Mrs. Zia presents lesson 15 from module 3, focusing on graphing solutions to inequalities. The lesson covers how to solve and graph inequalities, interpret solutions, and apply these skills to real-world problems. Examples include car sales, rental costs, clothing purchases, concert tickets, and earning money. Students learn to determine the direction of rays and whether endpoints are open or solid. The lesson emphasizes understanding inequalities in context and verifying solutions.

What is the primary goal of this lesson on graphing solutions to inequalities?

• To learn how to solve equations

• To memorize mathematical formulas

• To understand the properties of numbers

• To graph solutions to inequalities and interpret them

When graphing an inequality, what does an open circle on the number line indicate?

• The inequality is incorrect

• The number is not part of the solution

• The solution is a range of numbers

• The number is part of the solution

In the car dealership problem, what inequality represents the number of weeks needed to reduce the car inventory to less than 75?

• 525 + 50W < 75

• 525 - 50W < 75

• 525 - 50W > 75

• 525 + 50W > 75

For the car rental problem, what does 'no more than $525' translate to in terms of inequality?

• Less than or equal to $525

• Greater than $525

• Less than $525

• Equal to $525

In the sweater and jeans problem, what is the maximum price for each sweater if the total budget is $120?

• $35

• $25

• $40

• $28.33

How many balcony tickets must be bought at a minimum if the total tickets needed are at least 250?

• 250

• 165

• 80

• 200

What inequality represents the minimum number of hours Samuel must work to earn at least $29?

• 6h + 5 = 29

• 6h + 5 > 29

• 6h + 5 < 29

• 6h + 5 ≥ 29

What is the minimum number of hours Samuel must work to meet his goal?

• 4 hours

• 6 hours

• 5 hours

• 3 hours

What does a filled circle on a number line indicate when graphing inequalities?

• The solution is a range of numbers

• The inequality is incorrect

• The number is part of the solution

• The number is not part of the solution

What is the key takeaway from the lesson on graphing solutions to inequalities?

• Learning to graph and interpret inequalities

• Practicing basic arithmetic

• Understanding how to solve equations

• Memorizing mathematical formulas