Interpreting the Results of the Inequality

Oct 13, 2025 by thesweetdesigns.com 119 views

Understanding Inequalities and Their Applications

Inequalities are mathematical expressions that compare two values, indicating whether one is greater than, less than, or equal to the other. In the context of Cate's problem, we are given an inequality that represents the possible number of cats that a shelter can house. The inequality is represented as $c < 28$ , where $c$ is the number of cats that the shelter can accommodate.

The Importance of Inequalities in Real-World Scenarios

Inequalities have numerous applications in real-world scenarios, including finance, science, and engineering. In the context of Cate's problem, the inequality $c < 28$ provides a range of possible values for the number of cats that the shelter can house. This information is crucial in determining the capacity of the shelter and making informed decisions about the number of cats that can be accommodated.

Solving Inequalities: A Step-by-Step Approach

To solve an inequality, we need to isolate the variable on one side of the inequality sign. In this case, the variable is $c$ , and the inequality is $c < 28$ . To isolate $c$ , we can subtract 28 from both sides of the inequality, resulting in $c - 28 < 0$ . This inequality indicates that the number of cats that the shelter can house is less than 28.

Interpreting the Results of the Inequality

The inequality $c < 28$ provides a range of possible values for the number of cats that the shelter can house. This range includes all values less than 28, such as 0, 1, 2, 3, and so on. In other words, the shelter can house any number of cats that is less than 28.

Possible Solutions to Cate's Problem

Given the inequality $c < 28$ , a possible solution to Cate's problem is that the shelter can house 27 cats. This solution satisfies the inequality, as 27 is less than 28. Another possible solution is that the shelter can house 0 cats, as 0 is also less than 28.

Conclusion

In conclusion, the inequality $c < 28$ provides a range of possible values for the number of cats that a shelter can house. By solving the inequality, we can determine the capacity of the shelter and make informed decisions about the number of cats that can be accommodated. The possible solutions to Cate's problem include any number of cats that is less than 28, such as 27 or 0.

Answer to the Question

The statement that best describes a possible solution to Cate's problem is:

The shelter can house 27 cats.

This solution satisfies the inequality $c < 28$ , as 27 is less than 28.

Additional Examples and Applications

Inequalities have numerous applications in real-world scenarios, including finance, science, and engineering. Here are a few additional examples and applications of inequalities:

Finance: Inequalities can be used to determine the minimum or maximum amount of money that can be invested in a particular investment.
Science: Inequalities can be used to determine the minimum or maximum temperature that can be achieved in a particular experiment.
Engineering: Inequalities can be used to determine the minimum or maximum stress that can be applied to a particular material.

Tips and Tricks for Solving Inequalities

Here are a few tips and tricks for solving inequalities:

Isolate the variable: To solve an inequality, we need to isolate the variable on one side of the inequality sign.
Use inverse operations: To isolate the variable, we can use inverse operations, such as addition, subtraction, multiplication, and division.
Check the solution: Once we have isolated the variable, we need to check the solution to ensure that it satisfies the inequality.

Conclusion

In conclusion, inequalities are mathematical expressions that compare two values, indicating whether one is greater than, less than, or equal to the other. In the context of Cate's problem, the inequality $c < 28$ provides a range of possible values for the number of cats that a shelter can house. By solving the inequality, we can determine the capacity of the shelter and make informed decisions about the number of cats that can be accommodated.

Q: What is an inequality, and how is it used in real-world scenarios?

A: An inequality is a mathematical expression that compares two values, indicating whether one is greater than, less than, or equal to the other. Inequalities have numerous applications in real-world scenarios, including finance, science, and engineering. In the context of Cate's problem, the inequality $c < 28$ provides a range of possible values for the number of cats that a shelter can house.

Q: How do I solve an inequality, and what are the steps involved?

A: To solve an inequality, we need to isolate the variable on one side of the inequality sign. The steps involved in solving an inequality are:

Isolate the variable: To solve an inequality, we need to isolate the variable on one side of the inequality sign.
Use inverse operations: To isolate the variable, we can use inverse operations, such as addition, subtraction, multiplication, and division.
Check the solution: Once we have isolated the variable, we need to check the solution to ensure that it satisfies the inequality.

Q: What is the difference between an inequality and an equation?

A: An equation is a mathematical expression that states that two values are equal. An inequality, on the other hand, states that two values are not equal, but one is greater than, less than, or equal to the other.

Q: Can you provide an example of an inequality in a real-world scenario?

A: Yes, here is an example of an inequality in a real-world scenario:

Finance: A bank has a minimum balance requirement of $1,000 for a savings account. If the balance is less than $1,000, the account will be charged a monthly fee. In this case, the inequality is $b < 1,000, where $b$ is the balance in the account.

Q: How do I determine the capacity of a shelter based on an inequality?

A: To determine the capacity of a shelter based on an inequality, we need to isolate the variable on one side of the inequality sign. In the case of Cate's problem, the inequality $c < 28$ indicates that the shelter can house any number of cats that is less than 28.

Q: Can you provide an example of a possible solution to Cate's problem?

A: Yes, here is an example of a possible solution to Cate's problem:

The shelter can house 27 cats. This solution satisfies the inequality $c < 28$ , as 27 is less than 28.

Q: What are some tips and tricks for solving inequalities?

A: Here are a few tips and tricks for solving inequalities:

Isolate the variable: To solve an inequality, we need to isolate the variable on one side of the inequality sign.
Use inverse operations: To isolate the variable, we can use inverse operations, such as addition, subtraction, multiplication, and division.
Check the solution: Once we have isolated the variable, we need to check the solution to ensure that it satisfies the inequality.

Q: Can you provide an example of an inequality in a science scenario?

A: Yes, here is an example of an inequality in a science scenario:

Science: A scientist is conducting an experiment to determine the minimum temperature required to achieve a certain chemical reaction. The inequality is $t > 20$ , where $t$ is the temperature in degrees Celsius.

Q: How do I determine the minimum or maximum value of a variable based on an inequality?

A: To determine the minimum or maximum value of a variable based on an inequality, we need to isolate the variable on one side of the inequality sign. In the case of the inequality $t > 20$ , the minimum value of $t$ is 20, as any value less than 20 will not satisfy the inequality.

Q: Can you provide an example of an inequality in an engineering scenario?

A: Yes, here is an example of an inequality in an engineering scenario:

Engineering: An engineer is designing a bridge that can withstand a maximum stress of 10,000 pounds per square inch (PSI). The inequality is $s < 10,000$ , where $s$ is the stress in PSI.

Q: How do I determine the maximum value of a variable based on an inequality?

A: To determine the maximum value of a variable based on an inequality, we need to isolate the variable on one side of the inequality sign. In the case of the inequality $s < 10,000$ , the maximum value of $s$ is 10,000, as any value greater than 10,000 will not satisfy the inequality.