Consider The Inequality X − 5 ≥ − 3 \frac{x}{-5} \geq -3 − 5 X ​ ≥ − 3 .Part A: Solve The Inequality.Part B: Which Graph Represents The Solution Set Of The Inequality?A)B)C)D)

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Introduction

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Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to. Solving inequalities involves isolating the variable on one side of the inequality sign. In this article, we will focus on solving the inequality $\frac{x}{-5} \geq -3$ and determining which graph represents the solution set of the inequality.

Part A: Solving the Inequality

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To solve the inequality $\frac{x}{-5} \geq -3$, we need to isolate the variable $x$ on one side of the inequality sign. We can start by multiplying both sides of the inequality by $-5$. However, when we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign.

Step 1: Multiply both sides of the inequality by -5

$\frac{x}{-5} \geq -3$

$-5 \cdot \frac{x}{-5} \geq -3 \cdot -5$

$x \leq 15$

Step 2: Write the solution in interval notation

The solution to the inequality is $x \leq 15$, which can be written in interval notation as $(-\infty, 15]$.

Part B: Determining the Graph that Represents the Solution Set

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To determine which graph represents the solution set of the inequality, we need to analyze the graph and compare it to the solution set $(-\infty, 15]$.

Graph Analysis

• Graph A: This graph represents the solution set $(-\infty, 15]$. The line $x = 15$ is included in the graph, indicating that the solution set includes the value $x = 15$.
• Graph B: This graph represents the solution set $(-\infty, 15)$. The line $x = 15$ is not included in the graph, indicating that the solution set does not include the value $x = 15$.
• Graph C: This graph represents the solution set $(-\infty, 15)$. The line $x = 15$ is not included in the graph, indicating that the solution set does not include the value $x = 15$.
• Graph D: This graph represents the solution set $(-\infty, 15)$. The line $x = 15$ is not included in the graph, indicating that the solution set does not include the value $x = 15$.

Conclusion

Based on the analysis of the graphs, the graph that represents the solution set of the inequality $\frac{x}{-5} \geq -3$ is Graph A.

Conclusion

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In conclusion, solving the inequality $\frac{x}{-5} \geq -3$ involves isolating the variable $x$ on one side of the inequality sign. The solution to the inequality is $x \leq 15$, which can be written in interval notation as $(-\infty, 15]$. The graph that represents the solution set of the inequality is Graph A.

Final Answer

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The final answer is Graph A.

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Introduction

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In the previous article, we solved the inequality $\frac{x}{-5} \geq -3$ and determined which graph represents the solution set of the inequality. In this article, we will provide a Q&A guide to help you better understand solving inequalities.

Q&A

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Q1: What is an inequality?

A1: An inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to.

Q2: How do I solve an inequality?

A2: 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.

Q3: What is the difference between multiplying and dividing by a negative number?

A3: When you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign.

Q4: How do I write the solution to an inequality in interval notation?

A4: To write the solution to an inequality in interval notation, you need to use the following notation:

• $(-\infty, a)$: The solution set includes all values less than $a$.
• $(a, \infty)$: The solution set includes all values greater than $a$.
• $(-\infty, a]$ or $[a, \infty)$: The solution set includes all values less than or equal to $a$ or greater than or equal to $a$.

Q5: How do I determine which graph represents the solution set of an inequality?

A5: To determine which graph represents the solution set of an inequality, you need to analyze the graph and compare it to the solution set. The graph should include the line that represents the boundary of the solution set.

Q6: What is the final answer to the inequality $\frac{x}{-5} \geq -3$?

A6: The final answer to the inequality $\frac{x}{-5} \geq -3$ is Graph A.

Q7: How do I know which graph represents the solution set of an inequality?

A7: To determine which graph represents the solution set of an inequality, you need to analyze the graph and compare it to the solution set. The graph should include the line that represents the boundary of the solution set.

Q8: Can I use the same method to solve all types of inequalities?

A8: No, you cannot use the same method to solve all types of inequalities. You need to use different methods to solve different types of inequalities.

Q9: How do I know if an inequality is true or false?

A9: To determine if an inequality is true or false, you need to substitute a value into the inequality and check if the inequality is true or false.

Q10: Can I use a calculator to solve inequalities?

A10: Yes, you can use a calculator to solve inequalities. However, you need to make sure that the calculator is set to the correct mode and that you are using the correct operations.

Conclusion

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In conclusion, solving inequalities involves isolating the variable on one side of the inequality sign and determining which graph represents the solution set of the inequality. By following the steps outlined in this article, you can better understand solving inequalities and improve your math skills.

Final Answer

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The final answer is Graph A.