Solve The Following Inequality:$6.3r \ \textless \ -45.36$Which Graph Shows The Correct Solution?

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Introduction

In this article, we will delve into solving the given inequality 6.3r \textless −45.366.3r \ \textless \ -45.36 and determine which graph shows the correct solution. To begin, we need to understand the concept of inequalities and how to solve them. An inequality is a statement that two expressions are not equal, and it can be represented using various symbols such as <<, >>, ≤\leq, or ≥\geq. In this case, we are dealing with a linear inequality, which involves a linear expression on one side of the inequality symbol and a constant on the other side.

Understanding the Inequality

The given inequality is 6.3r \textless −45.366.3r \ \textless \ -45.36. To solve this inequality, we need to isolate the variable rr on one side of the inequality symbol. We can start by dividing both sides of the inequality by 6.36.3. This will give us the value of rr that satisfies the inequality.

Solving the Inequality

To solve the inequality, we need to follow the order of operations (PEMDAS):

  1. Divide both sides of the inequality by 6.36.3:

6.3r6.3 \textless −45.366.3\frac{6.3r}{6.3} \ \textless \ \frac{-45.36}{6.3}

  1. Simplify the expressions:

r \textless −7.22r \ \textless \ -7.22

Graphing the Solution

Now that we have solved the inequality, we need to determine which graph shows the correct solution. To do this, we need to understand the concept of graphing inequalities. When graphing an inequality, we need to consider the direction of the inequality symbol. If the inequality symbol is <<, we need to shade the region below the line. If the inequality symbol is >>, we need to shade the region above the line.

Graph 1: r \textless −7.22r \ \textless \ -7.22

Graph 1 shows the region below the line r=−7.22r = -7.22. This graph represents the solution to the inequality r \textless −7.22r \ \textless \ -7.22.

Graph 2: r \textgreater −7.22r \ \textgreater \ -7.22

Graph 2 shows the region above the line r=−7.22r = -7.22. This graph represents the solution to the inequality r \textgreater −7.22r \ \textgreater \ -7.22.

Graph 3: r \textless −7.22r \ \textless \ -7.22 and r \textgreater −7.22r \ \textgreater \ -7.22

Graph 3 shows the region below the line r=−7.22r = -7.22 and above the line r=−7.22r = -7.22. This graph represents the solution to the inequality r \textless −7.22r \ \textless \ -7.22 and r \textgreater −7.22r \ \textgreater \ -7.22.

Conclusion

In conclusion, the correct graph that shows the solution to the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36 is Graph 1: r \textless −7.22r \ \textless \ -7.22. This graph represents the region below the line r=−7.22r = -7.22, which is the solution to the inequality.

Final Answer

The final answer is Graph 1: r \textless −7.22r \ \textless \ -7.22.

Frequently Asked Questions

  • Q: What is the solution to the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36? A: The solution to the inequality is r \textless −7.22r \ \textless \ -7.22.
  • Q: Which graph shows the correct solution? A: Graph 1: r \textless −7.22r \ \textless \ -7.22 shows the correct solution.

References

  • [1] "Inequalities" by Khan Academy
  • [2] "Graphing Inequalities" by Mathway

Additional Resources

  • [1] "Inequalities" by Wolfram MathWorld
  • [2] "Graphing Inequalities" by Purplemath

Introduction

In our previous article, we solved the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36 and determined that the correct graph that shows the solution is Graph 1: r \textless −7.22r \ \textless \ -7.22. In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have.

Q&A

Q: What is the solution to the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36?

A: The solution to the inequality is r \textless −7.22r \ \textless \ -7.22.

Q: How do I graph the solution to the inequality?

A: To graph the solution, you need to shade the region below the line r=−7.22r = -7.22. This represents the solution to the inequality r \textless −7.22r \ \textless \ -7.22.

Q: What is the difference between the inequality r \textless −7.22r \ \textless \ -7.22 and the inequality r \textgreater −7.22r \ \textgreater \ -7.22?

A: The inequality r \textless −7.22r \ \textless \ -7.22 represents the region below the line r=−7.22r = -7.22, while the inequality r \textgreater −7.22r \ \textgreater \ -7.22 represents the region above the line r=−7.22r = -7.22.

Q: How do I determine which graph shows the correct solution?

A: To determine which graph shows the correct solution, you need to consider the direction of the inequality symbol. If the inequality symbol is <<, you need to shade the region below the line. If the inequality symbol is >>, you need to shade the region above the line.

Q: What is the final answer to the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36?

A: The final answer to the inequality is Graph 1: r \textless −7.22r \ \textless \ -7.22.

Q: Can I use a calculator to solve the inequality?

A: Yes, you can use a calculator to solve the inequality. However, you need to make sure that you are using the correct calculator and that you are entering the correct values.

Q: How do I check my answer to the inequality?

A: To check your answer, you need to substitute the value of rr into the original inequality and see if it is true. If it is true, then your answer is correct.

Conclusion

In conclusion, we hope that this Q&A article has helped to clarify any doubts or questions that readers may have had about solving the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36. If you have any further questions or concerns, please don't hesitate to contact us.

Final Answer

The final answer is Graph 1: r \textless −7.22r \ \textless \ -7.22.

Frequently Asked Questions

  • Q: What is the solution to the inequality 6.3r \textless −45.366.3r \ \textless \ -45.36? A: The solution to the inequality is r \textless −7.22r \ \textless \ -7.22.
  • Q: Which graph shows the correct solution? A: Graph 1: r \textless −7.22r \ \textless \ -7.22 shows the correct solution.

References

  • [1] "Inequalities" by Khan Academy
  • [2] "Graphing Inequalities" by Mathway

Additional Resources

  • [1] "Inequalities" by Wolfram MathWorld
  • [2] "Graphing Inequalities" by Purplemath