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

Introduction to Inequalities

In mathematics, inequalities are used to compare two or more values. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will focus on solving inequalities and graphing them on a number line. We will use the example of Cecilia, who correctly solved the inequality $3x > 102$ and $x > 34$. Our goal is to determine which graph matches the inequality.

Understanding 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. This gives us $x > 34$. This means that any value of $x$ that is greater than 34 will satisfy the inequality.

Graphing the Inequality

To graph the inequality on a number line, we need to plot a point on the number line that represents the value of $x$. In this case, we will plot the point 34 on the number line. Since the inequality is greater than 34, we will use an open circle to represent the point. This is because the inequality is not equal to 34, but rather greater than 34.

Types of Graphs

There are two types of graphs that can be used to represent an inequality on a number line: open circle and closed circle. An open circle is used to represent an inequality that is not equal to the value, while a closed circle is used to represent an inequality that is equal to the value.

Graph 1: Open Circle

The first graph is an open circle at the point 34 on the number line. This graph represents the inequality $x > 34$. Since the inequality is greater than 34, we use an open circle to represent the point.

Graph 2: Closed Circle

The second graph is a closed circle at the point 34 on the number line. This graph represents the inequality $x = 34$. Since the inequality is equal to 34, we use a closed circle to represent the point.

Graph 3: Open Circle with an Arrow

The third graph is an open circle at the point 34 on the number line, with an arrow pointing to the right. This graph represents the inequality $x > 34$. Since the inequality is greater than 34, we use an open circle to represent the point and an arrow to indicate that the inequality extends to the right.

Graph 4: Closed Circle with an Arrow

The fourth graph is a closed circle at the point 34 on the number line, with an arrow pointing to the right. This graph represents the inequality $x = 34$. Since the inequality is equal to 34, we use a closed circle to represent the point and an arrow to indicate that the inequality extends to the right.

Conclusion

In conclusion, the correct graph that matches the inequality $x > 34$ is the open circle with an arrow pointing to the right. This graph represents the inequality correctly, with an open circle at the point 34 and an arrow pointing to the right to indicate that the inequality extends to the right.

Frequently Asked Questions

• What is an inequality? An inequality is a statement that compares two or more values using a mathematical symbol such as >, <, ≥, or ≤.
• How do I graph an inequality on a number line? To graph an inequality on a number line, you need to plot a point on the number line that represents the value of the variable. You then use an open circle or a closed circle to represent the inequality, depending on whether the inequality is greater than, less than, equal to, or a combination of these.
• What is the difference between an open circle and a closed circle on a number line? An open circle is used to represent an inequality that is not equal to the value, while a closed circle is used to represent an inequality that is equal to the value.

Final Answer

The final answer is: Graph 3: Open Circle with an Arrow

Introduction

In our previous article, we discussed how to solve the inequality $3x > 102$ and $x > 34$. We also explored the different types of graphs that can be used to represent an inequality on a number line. In this article, we will provide a Q&A section to help you better understand the concepts and solve similar inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a statement that compares two or more values using a mathematical symbol such as >, <, ≥, or ≤.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding, subtracting, multiplying, or dividing both sides of the inequality by the same value.

Q: What is the difference between an open circle and a closed circle on a number line?

A: An open circle is used to represent an inequality that is not equal to the value, while a closed circle is used to represent an inequality that is equal to the value.

Q: How do I graph an inequality on a number line?

A: To graph an inequality on a number line, you need to plot a point on the number line that represents the value of the variable. You then use an open circle or a closed circle to represent the inequality, depending on whether the inequality is greater than, less than, equal to, or a combination of these.

Q: What is the meaning of the inequality $x > 34$?

A: The inequality $x > 34$ means that any value of $x$ that is greater than 34 will satisfy the inequality.

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

A: To determine which graph matches the inequality, you need to look at the inequality sign and the value of the variable. If the inequality sign is >, you will use an open circle with an arrow pointing to the right. If the inequality sign is <, you will use an open circle with an arrow pointing to the left.

Q: Can I use a closed circle to represent an inequality that is not equal to the value?

A: No, you cannot use a closed circle to represent an inequality that is not equal to the value. A closed circle is used to represent an inequality that is equal to the value.

Q: How do I graph an inequality with multiple values?

A: To graph an inequality with multiple values, you need to plot multiple points on the number line that represent the different values of the variable. You then use open circles or closed circles to represent the inequality, depending on whether the inequality is greater than, less than, equal to, or a combination of these.

Q: Can I use a number line to graph an inequality with negative values?

A: Yes, you can use a number line to graph an inequality with negative values. You will need to plot the negative values on the number line and use open circles or closed circles to represent the inequality.

Conclusion

In conclusion, solving inequalities and graphing them on a number line can be a challenging task, but with practice and patience, you can become proficient in solving these types of problems. Remember to always follow the steps outlined in this article and to use the correct symbols and notation to represent the inequality.

Frequently Asked Questions

• What is the difference between an inequality and an equation? An inequality is a statement that compares two or more values using a mathematical symbol such as >, <, ≥, or ≤, while an equation is a statement that states that two or more values are equal.
• How do I determine which graph matches the inequality? To determine which graph matches the inequality, you need to look at the inequality sign and the value of the variable. If the inequality sign is >, you will use an open circle with an arrow pointing to the right. If the inequality sign is <, you will use an open circle with an arrow pointing to the left.
• Can I use a closed circle to represent an inequality that is not equal to the value? No, you cannot use a closed circle to represent an inequality that is not equal to the value. A closed circle is used to represent an inequality that is equal to the value.

Final Answer

The final answer is: Graph 3: Open Circle with an Arrow