Cecilia Correctly Solved This Inequality:${ \begin{aligned} 3x & \ \textgreater \ 102 \ x & \ \textgreater \ 34 \end{aligned} }$Which Graph Matches The Inequality?

Introduction to Inequalities

Inequalities are mathematical expressions that compare two values, indicating whether one is greater than, less than, or equal to the other. They are a fundamental concept in mathematics, and understanding how to solve and graph inequalities is crucial for success in algebra and beyond. In this article, we will explore how to solve and graph the inequality $3x > 102$, and then determine which graph matches the inequality.

Solving the Inequality

To solve the inequality $3x > 102$, we need to isolate the variable $x$. We can do this by dividing both sides of the inequality by 3. However, when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.

{ \begin{aligned} 3x & \ \textgreater \ 102 \\ x & \ \textgreater \ 34 \end{aligned} \}

Understanding the Graph

A graph is a visual representation of the solution to an inequality. In this case, we are looking for a graph that represents the solution to the inequality $x > 34$. To create a graph, we need to determine the x-intercept, which is the point where the graph intersects the x-axis. In this case, the x-intercept is 34.

Types of Graphs

There are several types of graphs that can represent the solution to an inequality. The most common types of graphs are:

• Solid Line Graph: A solid line graph represents the solution to an inequality as a continuous line.
• Dashed Line Graph: A dashed line graph represents the solution to an inequality as a dashed line.
• Dotted Line Graph: A dotted line graph represents the solution to an inequality as a dotted line.

Graphing the Inequality

To graph the inequality $x > 34$, we need to draw a solid line at x = 34 and shade the region to the right of the line. This represents the solution to the inequality.

Determining the Correct Graph

Now that we have created a graph representing the solution to the inequality $x > 34$, we need to determine which graph matches the inequality. Let's examine the options:

• Graph A: A solid line graph with a shaded region to the right of the line.
• Graph B: A dashed line graph with a shaded region to the right of the line.
• Graph C: A dotted line graph with a shaded region to the right of the line.

Conclusion

Based on our analysis, the correct graph that matches the inequality $x > 34$ is Graph A: A solid line graph with a shaded region to the right of the line. This graph accurately represents the solution to the inequality, and it is the only graph that matches the inequality.

Final Thoughts

In conclusion, solving and graphing inequalities is a crucial concept in mathematics. By understanding how to solve and graph inequalities, we can better represent the solution to an inequality and make informed decisions. In this article, we explored how to solve and graph the inequality $3x > 102$, and then determined which graph matches the inequality. We hope that this article has provided valuable insights and information on solving and graphing inequalities.

Frequently Asked Questions

• Q: What is an inequality? A: An inequality is a mathematical expression that compares two values, indicating whether one is greater than, less than, or equal to the other.
• Q: How do I solve an inequality? A: To solve an inequality, you need to isolate the variable by performing operations on both sides of the inequality.
• Q: What is a graph? A: A graph is a visual representation of the solution to an inequality.
• Q: What types of graphs can represent the solution to an inequality? A: There are several types of graphs that can represent the solution to an inequality, including solid line graphs, dashed line graphs, and dotted line graphs.

References

• Algebra and Trigonometry by Michael Sullivan
• Mathematics for the Nonmathematician by Morris Kline
• Graphing Inequalities by Math Open Reference

Additional Resources

• Graphing Inequalities by Khan Academy
• Solving Inequalities by Mathway
• Graphing Inequalities by IXL
  

Introduction

In our previous article, we explored how to solve and graph the inequality $3x > 102$, and then determined which graph matches the inequality. In this article, we will answer some frequently asked questions about solving and graphing inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values, indicating whether one is greater than, less than, or equal to the other.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable by performing operations on both sides of the inequality. For example, to solve the inequality $3x > 102$, you would divide both sides by 3 to get $x > 34$.

Q: What is a graph?

A: A graph is a visual representation of the solution to an inequality. It is a way to represent the solution to an inequality in a graphical format.

Q: What types of graphs can represent the solution to an inequality?

A: There are several types of graphs that can represent the solution to an inequality, including:

• Solid Line Graph: A solid line graph represents the solution to an inequality as a continuous line.
• Dashed Line Graph: A dashed line graph represents the solution to an inequality as a dashed line.
• Dotted Line Graph: A dotted line graph represents the solution to an inequality as a dotted line.

Q: How do I determine which graph matches the inequality?

A: To determine which graph matches the inequality, you need to examine the graph and determine which type of graph it is. For example, if the graph is a solid line graph with a shaded region to the right of the line, it is likely that the graph matches the inequality.

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

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

• Not isolating the variable: Make sure to isolate the variable by performing operations on both sides of the inequality.
• Not considering the direction of the inequality: Make sure to consider the direction of the inequality when solving and graphing the inequality.
• Not using the correct type of graph: Make sure to use the correct type of graph to represent the solution to the inequality.

Q: How can I practice solving and graphing inequalities?

A: There are several ways to practice solving and graphing inequalities, including:

• Using online resources: There are many online resources available that provide practice problems and examples for solving and graphing inequalities.
• Working with a tutor: Working with a tutor can provide one-on-one instruction and practice for solving and graphing inequalities.
• Using graphing software: Graphing software can provide a visual representation of the solution to an inequality and can be used to practice solving and graphing inequalities.

Conclusion

In conclusion, solving and graphing inequalities is a crucial concept in mathematics. By understanding how to solve and graph inequalities, we can better represent the solution to an inequality and make informed decisions. In this article, we answered some frequently asked questions about solving and graphing inequalities, and provided some tips and resources for practicing solving and graphing inequalities.

Final Thoughts

In conclusion, solving and graphing inequalities is a complex and nuanced topic. By understanding the concepts and techniques involved, we can better represent the solution to an inequality and make informed decisions. We hope that this article has provided valuable insights and information on solving and graphing inequalities.

Frequently Asked Questions

• Q: What is an inequality? A: An inequality is a mathematical expression that compares two values, indicating whether one is greater than, less than, or equal to the other.
• Q: How do I solve an inequality? A: To solve an inequality, you need to isolate the variable by performing operations on both sides of the inequality.
• Q: What is a graph? A: A graph is a visual representation of the solution to an inequality.
• Q: What types of graphs can represent the solution to an inequality? A: There are several types of graphs that can represent the solution to an inequality, including solid line graphs, dashed line graphs, and dotted line graphs.

References

• Algebra and Trigonometry by Michael Sullivan
• Mathematics for the Nonmathematician by Morris Kline
• Graphing Inequalities by Math Open Reference

Additional Resources

• Graphing Inequalities by Khan Academy
• Solving Inequalities by Mathway
• Graphing Inequalities by IXL