For One Photography Session, Dexter Earns No Less Than $\$50$, But No More Than $\$100$. Which Inequality Can Be Used To Represent His Earnings, $e$?A. $e \geq 50$ Or $e \leq 100$ B. $e \ \textgreater

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In mathematics, inequalities are used to represent various real-world scenarios where the relationship between two or more quantities is not fixed. In this article, we will explore how inequalities can be used to represent a specific scenario involving Dexter's photography earnings.

Dexter's Photography Earnings

Dexter is a photographer who earns a certain amount of money for each photography session he completes. The problem states that Dexter earns no less than $50\$50 and no more than $100\$100 for each session. This information can be represented using an inequality, which is a mathematical statement that describes the relationship between two or more quantities.

Representing Dexter's Earnings Using an Inequality

To represent Dexter's earnings using an inequality, we need to consider the two conditions given in the problem: Dexter earns no less than $50\$50 and no more than $100\$100. This can be represented using the following inequality:

50≤e≤10050 \leq e \leq 100

In this inequality, ee represents Dexter's earnings, and the inequality states that his earnings are greater than or equal to $50\$50 and less than or equal to $100\$100. This is a compound inequality, which is a combination of two or more inequalities joined by the word "and" or "or".

Alternative Representations

There are alternative ways to represent Dexter's earnings using an inequality. One way is to use the "or" condition, which is represented as:

e≥50e \geq 50 or e≤100e \leq 100

This inequality states that Dexter's earnings are either greater than or equal to $50\$50 or less than or equal to $100\$100. This is also a compound inequality, but it is represented using the "or" condition instead of the "and" condition.

Another Alternative Representation

Another alternative way to represent Dexter's earnings using an inequality is to use the "greater than" and "less than" conditions separately. This can be represented as:

50≤e<10050 \leq e < 100

In this inequality, the "less than" condition is used to represent the upper limit of Dexter's earnings, which is $100\$100. This is a single inequality, but it is represented using the "less than" condition instead of the "less than or equal to" condition.

Conclusion

In conclusion, Dexter's photography earnings can be represented using an inequality, which is a mathematical statement that describes the relationship between two or more quantities. The inequality can be represented in different ways, including using the "and" condition, the "or" condition, and the "greater than" and "less than" conditions separately. Each of these representations provides a different way to express the relationship between Dexter's earnings and the given conditions.

Key Takeaways

  • Inequalities are used to represent real-world scenarios where the relationship between two or more quantities is not fixed.
  • Dexter's photography earnings can be represented using an inequality, which is a mathematical statement that describes the relationship between two or more quantities.
  • The inequality can be represented in different ways, including using the "and" condition, the "or" condition, and the "greater than" and "less than" conditions separately.

Final Answer

In the previous article, we explored how inequalities can be used to represent real-world scenarios, including Dexter's photography earnings. In this article, we will answer some frequently asked questions (FAQs) about inequalities to provide a deeper understanding of this mathematical concept.

Q: What is an inequality?

A: An inequality is a mathematical statement that describes the relationship between two or more quantities. It is used to represent real-world scenarios where the relationship between two or more quantities is not fixed.

Q: What are the different types of inequalities?

A: There are several types of inequalities, including:

  • Linear inequalities: These are inequalities that involve a linear expression, such as x>2x > 2 or x<5x < 5.
  • Quadratic inequalities: These are inequalities that involve a quadratic expression, such as x2>4x^2 > 4 or x2<9x^2 < 9.
  • Compound inequalities: These are inequalities that involve two or more inequalities joined by the word "and" or "or", such as x>2x > 2 and x<5x < 5 or x>2x > 2 or x<5x < 5.

Q: How do I solve an inequality?

A: Solving an inequality involves finding the values of the variable that satisfy the inequality. Here are the steps to solve an inequality:

  1. Isolate the variable: Move all the terms containing the variable to one side of the inequality.
  2. Simplify the inequality: Simplify the inequality by combining like terms.
  3. Find the solution: Find the values of the variable that satisfy the inequality.

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

A: An equation is a mathematical statement that states that two or more quantities are equal. An inequality, on the other hand, is a mathematical statement that describes the relationship between two or more quantities, but does not state that they are equal.

Q: Can I use inequalities to represent real-world scenarios?

A: Yes, inequalities can be used to represent real-world scenarios where the relationship between two or more quantities is not fixed. For example, an inequality can be used to represent the cost of a product, the temperature of a room, or the number of people in a crowd.

Q: How do I graph an inequality?

A: Graphing an inequality involves plotting the solution on a number line or a coordinate plane. Here are the steps to graph an inequality:

  1. Plot the boundary: Plot the boundary of the inequality on a number line or a coordinate plane.
  2. Determine the direction: Determine the direction of the inequality by using a test point.
  3. Plot the solution: Plot the solution on a number line or a coordinate plane.

Q: Can I use inequalities to solve problems in other subjects?

A: Yes, inequalities can be used to solve problems in other subjects, such as algebra, geometry, and calculus. Inequalities are a fundamental concept in mathematics and are used to solve a wide range of problems.

Q: What are some real-world applications of inequalities?

A: Inequalities have many real-world applications, including:

  • Finance: Inequalities are used to calculate interest rates, investment returns, and credit scores.
  • Science: Inequalities are used to model population growth, chemical reactions, and physical systems.
  • Engineering: Inequalities are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

In conclusion, inequalities are a fundamental concept in mathematics that can be used to represent real-world scenarios and solve problems in other subjects. By understanding how to solve and graph inequalities, you can apply this knowledge to a wide range of problems and real-world applications.

Key Takeaways

  • Inequalities are used to represent real-world scenarios where the relationship between two or more quantities is not fixed.
  • Inequalities can be used to solve problems in other subjects, such as algebra, geometry, and calculus.
  • Inequalities have many real-world applications, including finance, science, and engineering.

Final Answer

The final answer is: Inequalitiesareafundamentalconceptinmathematicsthatcanbeusedtorepresentreal−worldscenariosandsolveproblemsinothersubjects.\boxed{Inequalities are a fundamental concept in mathematics that can be used to represent real-world scenarios and solve problems in other subjects.}