Write An Inequality To Model The Situation:Thomas Earned $$ 44$ Or More.A. T ≤ 44 T \leq 44 T ≤ 44 B. T ≥ 44 T \geq 44 T ≥ 44 C. T \textgreater 44 T \ \textgreater \ 44 T \textgreater 44 D. T \textless 44 T \ \textless \ 44 T \textless 44

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Introduction

Inequalities are mathematical expressions that compare two values, often used to model real-world situations. In this article, we will explore how to write an inequality to model a specific scenario involving Thomas's earnings. We will examine the different options and determine the correct inequality to represent the situation.

Understanding the Situation

Thomas earned $44 or more. This statement implies that Thomas's earnings are greater than or equal to $44. We need to write an inequality that represents this situation.

Option A: t≤44t \leq 44

This option states that Thomas's earnings are less than or equal to $44. However, this contradicts the given information that Thomas earned $44 or more. Therefore, option A is not the correct choice.

Option B: t≥44t \geq 44

This option states that Thomas's earnings are greater than or equal to $44. This aligns with the given information that Thomas earned $44 or more. Therefore, option B is a strong candidate for the correct answer.

Option C: t \textgreater 44t \ \textgreater \ 44

This option states that Thomas's earnings are greater than $44. However, this does not account for the possibility that Thomas earned exactly $44. Therefore, option C is not the correct choice.

Option D: t \textless 44t \ \textless \ 44

This option states that Thomas's earnings are less than $44. This contradicts the given information that Thomas earned $44 or more. Therefore, option D is not the correct choice.

Conclusion

Based on the analysis, the correct inequality to model the situation is t≥44t \geq 44. This inequality accurately represents the information that Thomas earned $44 or more.

Why is this important?

Understanding how to write inequalities to model real-world situations is crucial in mathematics and other fields. Inequalities are used to represent constraints, relationships, and patterns, making them essential tools for problem-solving and decision-making.

Real-World Applications

Inequalities have numerous real-world applications, including:

  • Finance: Inequalities are used to model financial transactions, investments, and risk management.
  • Science: Inequalities are used to model physical systems, such as population growth, chemical reactions, and electrical circuits.
  • Engineering: Inequalities are used to model design constraints, such as structural integrity, thermal management, and electrical safety.

Tips and Tricks

When writing inequalities, remember to:

  • Read carefully: Understand the given information and what is being asked.
  • Use variables: Represent unknown values with variables, such as tt.
  • Choose the correct symbol: Use the correct inequality symbol, such as ≥\geq or ≤\leq.
  • Check your work: Verify that the inequality accurately represents the given information.

Practice Problems

Try the following practice problems to reinforce your understanding of inequalities:

  1. Write an inequality to model the situation: "The temperature is 25°C or higher."
  2. Write an inequality to model the situation: "The cost of a product is $50 or less."
  3. Write an inequality to model the situation: "The number of students in a class is 20 or more."

Conclusion

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values, often used to model real-world situations. It is a statement that one value is greater than, less than, or equal to another value.

Q: What are the different types of inequalities?

A: There are four main types of inequalities:

  • Greater than: a>ba > b
  • Less than: a<ba < b
  • Greater than or equal to: a≥ba \geq b
  • Less than or equal to: a≤ba \leq b

Q: How do I write an inequality to model a situation?

A: To write an inequality to model a situation, follow these steps:

  1. Read carefully: Understand the given information and what is being asked.
  2. Identify the variable: Represent the unknown value with a variable, such as tt.
  3. Choose the correct symbol: Use the correct inequality symbol, such as ≥\geq or ≤\leq.
  4. Check your work: Verify that the inequality accurately represents the given information.

Q: What is the difference between a≥ba \geq b and a>ba > b?

A: The difference between a≥ba \geq b and a>ba > b is that a≥ba \geq b includes the possibility that aa is equal to bb, while a>ba > b does not.

Q: How do I solve an inequality?

A: To solve an inequality, follow these steps:

  1. Isolate the variable: Get the variable alone on one side of the inequality.
  2. Simplify the inequality: Simplify the inequality by combining like terms.
  3. Check your work: Verify that the solution accurately represents the given information.

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

A: The difference between solving an inequality and solving an equation is that solving an inequality involves finding all possible values of the variable, while solving an equation involves finding a single value of the variable.

Q: How do I graph an inequality?

A: To graph an inequality, follow these steps:

  1. Graph the boundary: Graph the line that represents the boundary of the inequality.
  2. Shade the region: Shade the region that represents the solution to the inequality.
  3. Label the graph: Label the graph with the inequality and the solution.

Q: What are some common mistakes to avoid when working with inequalities?

A: Some common mistakes to avoid when working with inequalities include:

  • Not reading carefully: Failing to read the problem carefully can lead to incorrect solutions.
  • Not choosing the correct symbol: Using the wrong inequality symbol can lead to incorrect solutions.
  • Not checking work: Failing to check work can lead to incorrect solutions.

Q: How do I apply inequalities to real-world problems?

A: To apply inequalities to real-world problems, follow these steps:

  1. Read the problem carefully: Understand the given information and what is being asked.
  2. Identify the variable: Represent the unknown value with a variable, such as tt.
  3. Choose the correct symbol: Use the correct inequality symbol, such as ≥\geq or ≤\leq.
  4. Check your work: Verify that the inequality accurately represents the given information.

Conclusion

In conclusion, inequalities are a powerful tool for modeling real-world situations and solving problems. By understanding the different types of inequalities, how to write an inequality to model a situation, and how to solve an inequality, you can apply inequalities to a wide range of problems. Remember to practice regularly and apply your knowledge to real-world applications.