Inequalities and Budgeting Problems

Mrs. Zia presents lesson 14 from module 3, focusing on solving inequalities. Students learn to solve word problems involving inequalities, interpret solutions, and understand when to reverse inequality symbols. The lesson includes examples such as a roller coaster profit problem, a summer camp budget issue, an exotic animal exhibit insurance rate, and a sales commission scenario. Key concepts include understanding revenue, expenses, and profit, as well as applying mathematical operations to solve inequalities.

What is the primary goal when solving an inequality?

• To eliminate all variables

• To find the exact value of the variable

• To determine the range of values for the variable

• To convert the inequality into an equation

In the roller coaster problem, what is the inequality used to find the minimum number of riders?

• 6P - 265 ≤ 11,000

• 6P + 265 ≤ 11,000

• 6P - 265 ≥ 11,000

• 6P + 265 ≥ 11,000

Why is it important to interpret the solution of an inequality in the context of the problem?

• To ensure the solution is a whole number

• To verify the solution is a decimal

• To check if the solution is zero

• To confirm the solution is negative

In the youth summer camp problem, what is the fixed cost that must be considered?

• $600 combined fixed cost

• $17.95 per camper

• $350 for transportation

• $250 for chaperons

What is the greatest number of campers that can attend the carnival while staying within budget?

• 76

• 77

• 78

• 79

In the exotic animal exhibit problem, what is the inequality used to find the maximum daily insurance rate?

• 650 - 5.5I > 500

• 650 + 5.5I > 500

• 650 - 5.5I < 500

• 650 + 5.5I < 500

What happens to the inequality symbol when dividing by a negative number?

• It remains the same

• It reverses

• It becomes an equation

• It disappears

In the sales commission problem, what percentage of sales is the commission?

• 20%

• 5%

• 15%

• 10%

What is the minimum amount of sales needed to earn more than $1,500?

• $25,000

• $15,000

• $18,000

• $20,000

What is the final step in solving an inequality?

• Undo multiplication or division

• Simplify using PMDO

• Interpret the answer

• Undo addition or subtraction