Select The Correct Inequalities.Franco Earns \[$\$8\$\] Per Hour At His After-school Job. Last Week, He Received A Paycheck Of More Than \[$\$168\$\]. If He Worked For \[$h\$\] Hours That Week, Find All The Inequalities That

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Introduction

In this article, we will delve into the world of inequalities and explore how to select the correct ones to solve a given problem. We will use the scenario of Franco, who earns $8 per hour at his after-school job, and received a paycheck of more than $168 last week. Our goal is to find all the inequalities that represent the number of hours he worked that week.

Understanding Inequalities

Inequalities are mathematical statements that compare two expressions, indicating whether one is greater than, less than, or equal to the other. They are used to represent a range of values or a set of possible solutions to a problem. In this case, we want to find the inequalities that represent the number of hours Franco worked that week.

The Problem

Franco earns $8 per hour at his after-school job. Last week, he received a paycheck of more than $168. If he worked for hh hours that week, we want to find all the inequalities that represent the number of hours he worked.

Step 1: Setting Up the Equation

To solve this problem, we need to set up an equation that represents the situation. Since Franco earns $8 per hour, the total amount he earned last week is 8h8h. We know that he received a paycheck of more than $168, so we can set up the following inequality:

8h>1688h > 168

This inequality represents the situation, but we need to find all the possible inequalities that represent the number of hours Franco worked.

Step 2: Solving the Inequality

To solve the inequality, we need to isolate the variable hh. We can do this by dividing both sides of the inequality by 8:

h>1688h > \frac{168}{8}

Simplifying the right-hand side, we get:

h>21h > 21

This inequality represents the minimum number of hours Franco worked that week.

Step 3: Finding the Other Inequalities

We know that the inequality h>21h > 21 represents the minimum number of hours Franco worked. However, we also need to consider the other possible inequalities that represent the number of hours he worked. Let's analyze the situation:

  • If Franco worked for 21 hours, he would have earned $168, which is the minimum amount he received.
  • If Franco worked for more than 21 hours, he would have earned more than $168.
  • If Franco worked for less than 21 hours, he would have earned less than $168.

Based on this analysis, we can conclude that the other possible inequalities are:

h≥21h \geq 21

h≤21h \leq 21

However, we need to be careful when selecting the correct inequalities. The inequality h≤21h \leq 21 is not correct, because it represents the situation where Franco worked for less than 21 hours, which is not possible given the information.

Conclusion

In conclusion, the correct inequalities that represent the number of hours Franco worked that week are:

h>21h > 21

h≥21h \geq 21

These inequalities represent the minimum number of hours Franco worked and the range of possible hours he worked.

Final Answer

The final answer is:

h>21h > 21

h≥21h \geq 21

Additional Information

  • The inequality h>21h > 21 represents the minimum number of hours Franco worked.
  • The inequality h≥21h \geq 21 represents the range of possible hours Franco worked.
  • The inequality h≤21h \leq 21 is not correct, because it represents the situation where Franco worked for less than 21 hours, which is not possible given the information.

References

Q: What is the main goal of this article?

A: The main goal of this article is to help readers understand how to select the correct inequalities to solve a given problem. We will use the scenario of Franco, who earns $8 per hour at his after-school job, and received a paycheck of more than $168 last week.

Q: What is the first step in solving this problem?

A: The first step in solving this problem is to set up an equation that represents the situation. Since Franco earns $8 per hour, the total amount he earned last week is 8h8h. We know that he received a paycheck of more than $168, so we can set up the following inequality:

8h>1688h > 168

Q: How do we solve the inequality?

A: To solve the inequality, we need to isolate the variable hh. We can do this by dividing both sides of the inequality by 8:

h>1688h > \frac{168}{8}

Simplifying the right-hand side, we get:

h>21h > 21

Q: What does the inequality h>21h > 21 represent?

A: The inequality h>21h > 21 represents the minimum number of hours Franco worked that week.

Q: What are the other possible inequalities that represent the number of hours Franco worked?

A: Based on the analysis, we can conclude that the other possible inequalities are:

h≥21h \geq 21

However, we need to be careful when selecting the correct inequalities. The inequality h≤21h \leq 21 is not correct, because it represents the situation where Franco worked for less than 21 hours, which is not possible given the information.

Q: Why is the inequality h≤21h \leq 21 not correct?

A: The inequality h≤21h \leq 21 is not correct because it represents the situation where Franco worked for less than 21 hours, which is not possible given the information. We know that Franco worked for more than 21 hours, so the correct inequality is h>21h > 21.

Q: What is the final answer?

A: The final answer is:

h>21h > 21

h≥21h \geq 21

Q: What is the main takeaway from this article?

A: The main takeaway from this article is that when solving inequalities, it's essential to carefully analyze the situation and select the correct inequalities to represent the problem.

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

A: Some common mistakes to avoid when solving inequalities include:

  • Not carefully analyzing the situation
  • Not selecting the correct inequalities to represent the problem
  • Not considering all possible solutions

Q: How can readers apply the concepts learned in this article to real-life situations?

A: Readers can apply the concepts learned in this article to real-life situations by:

  • Analyzing the situation carefully
  • Selecting the correct inequalities to represent the problem
  • Considering all possible solutions

By following these steps, readers can develop a deeper understanding of inequalities and apply the concepts to real-life situations.

Conclusion

In conclusion, selecting the correct inequalities is a crucial step in solving mathematical problems. By carefully analyzing the situation and selecting the correct inequalities, readers can develop a deeper understanding of inequalities and apply the concepts to real-life situations.