Which Graph Represents The Solution To The Inequality { -2.79 \leq 0.3x$}$?

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Introduction

In mathematics, inequalities are used to compare two values or expressions. 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 the inequality ${-2.79 \leq 0.3x}$ and determining which graph represents the solution.

Understanding the Inequality

The given inequality is ${-2.79 \leq 0.3x}$. To solve this inequality, we need to isolate the variable x. We can start by dividing both sides of the inequality by 0.3. This will give us the value of x 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 0.3: ${-2.79 \leq 0.3x}$ ${\frac{-2.79}{0.3} \leq x}$ ${-9.3 \leq x}$

Graphing the Solution

Now that we have the solution to the inequality, we can graph it on a number line. The number line is a visual representation of the solution set. We can use a number line to determine which graph represents the solution to the inequality.

Graph 1: Closed Circle at -9.3

The first graph is a closed circle at -9.3. This graph represents the solution to the inequality ${-9.3 \leq x}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 2: Open Circle at -9.3

The second graph is an open circle at -9.3. This graph represents the solution to the inequality ${x < -9.3}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 3: Closed Circle at -9.3 and Open Circle at Infinity

The third graph is a closed circle at -9.3 and an open circle at infinity. This graph represents the solution to the inequality ${-9.3 \leq x < \infty}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 4: Closed Circle at -9.3 and Closed Circle at Infinity

The fourth graph is a closed circle at -9.3 and a closed circle at infinity. This graph represents the solution to the inequality ${-9.3 \leq x \leq \infty}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 5: Closed Circle at -9.3 and Open Circle at -Infinity

The fifth graph is a closed circle at -9.3 and an open circle at negative infinity. This graph represents the solution to the inequality ${-\infty < x \leq -9.3}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 6: Closed Circle at -9.3 and Closed Circle at -Infinity

The sixth graph is a closed circle at -9.3 and a closed circle at negative infinity. This graph represents the solution to the inequality ${-\infty < x \leq -9.3}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 7: Closed Circle at -9.3 and Open Circle at Infinity

The seventh graph is a closed circle at -9.3 and an open circle at infinity. This graph represents the solution to the inequality ${-9.3 \leq x < \infty}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 8: Closed Circle at -9.3 and Closed Circle at Infinity

The eighth graph is a closed circle at -9.3 and a closed circle at infinity. This graph represents the solution to the inequality ${-9.3 \leq x \leq \infty}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 9: Closed Circle at -9.3 and Open Circle at -Infinity

The ninth graph is a closed circle at -9.3 and an open circle at negative infinity. This graph represents the solution to the inequality ${-\infty < x \leq -9.3}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Graph 10: Closed Circle at -9.3 and Closed Circle at -Infinity

The tenth graph is a closed circle at -9.3 and a closed circle at negative infinity. This graph represents the solution to the inequality ${-\infty < x \leq -9.3}$. However, this graph does not represent the solution to the original inequality ${-2.79 \leq 0.3x}$.

Conclusion

After analyzing all the graphs, we can conclude that none of the graphs represent the solution to the original inequality ${-2.79 \leq 0.3x}$. The correct graph is not among the options provided. However, we can use the solution to the inequality to determine which graph represents the solution to the inequality ${-9.3 \leq x}$.

Final Answer

The final answer is not among the options provided. However, we can use the solution to the inequality to determine which graph represents the solution to the inequality ${-9.3 \leq x}$.

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Introduction

In our previous article, we discussed solving the inequality ${-2.79 \leq 0.3x}$ and determining which graph represents the solution. However, we realized that none of the graphs provided represent the solution to the original inequality. In this article, we will answer some frequently asked questions about solving the inequality and provide additional information to help you understand the concept.

Q: What is the solution to the inequality ${-2.79 \leq 0.3x}$?

A: The solution to the inequality is ${-9.3 \leq x}$. This means that the value of x must be greater than or equal to -9.3.

Q: How do I graph the solution on a number line?

A: To graph the solution on a number line, you can use a closed circle at -9.3 to represent the lower bound of the solution set. You can also use an open circle at infinity to represent the upper bound of the solution set.

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

A: A closed circle on a number line represents a value that is included in the solution set, while an open circle represents a value that is not included in the solution set.

Q: How do I determine which graph represents the solution to the inequality?

A: To determine which graph represents the solution to the inequality, you need to analyze the graph and compare it to the solution set. If the graph includes the value -9.3 and extends to infinity, then it represents the solution to the inequality.

Q: What if the graph does not include the value -9.3 or extends to negative infinity?

A: If the graph does not include the value -9.3 or extends to negative infinity, then it does not represent the solution to the inequality.

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

A: Yes, you can use a graphing calculator to solve the inequality. Simply enter the inequality into the calculator and use the graphing function to visualize the solution set.

Q: How do I enter the inequality into a graphing calculator?

A: To enter the inequality into a graphing calculator, you need to follow the calculator's instructions for entering inequalities. Typically, you will need to enter the inequality in the form of y = f(x), where f(x) is the expression on the right-hand side of the inequality.

Q: What if I get an error message when entering the inequality into a graphing calculator?

A: If you get an error message when entering the inequality into a graphing calculator, it may be due to a syntax error or a formatting issue. Check the calculator's instructions for entering inequalities and try again.

Q: Can I use a graphing calculator to determine which graph represents the solution to the inequality?

A: Yes, you can use a graphing calculator to determine which graph represents the solution to the inequality. Simply enter the inequality into the calculator and use the graphing function to visualize the solution set. Then, compare the graph to the options provided to determine which one represents the solution.

Conclusion

Solving the inequality ${-2.79 \leq 0.3x}$ requires careful analysis and attention to detail. By following the steps outlined in this article, you can determine the solution to the inequality and identify which graph represents the solution. Remember to use a graphing calculator if you need help visualizing the solution set.