Which Choice Is The Solution To The Inequality Below? 7 X \textgreater 77 7x \ \textgreater \ 77 7 X \textgreater 77 A. X ≥ 77 X \geq 77 X ≥ 77 B. X \textgreater 77 X \ \textgreater \ 77 X \textgreater 77 C. X \textless 11 X \ \textless \ 11 X \textless 11 D. X \textgreater 11 X \ \textgreater \ 11 X \textgreater 11

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Introduction

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In mathematics, inequalities are a fundamental concept that deals with the comparison of two or more values. They are used to represent relationships between variables and are essential in solving various mathematical problems. In this article, we will focus on solving the inequality $7x > 77$ and determine the correct solution among the given options.

Understanding Inequalities

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An inequality is a statement that compares two or more values using a mathematical symbol, such as greater than ($>$), less than ($<$), greater than or equal to ($\geq$), or less than or equal to ($\leq$). In the given inequality $7x > 77$, we are comparing the product of $7$ and $x$ with $77$. The goal is to find the value of $x$ that satisfies this inequality.

Solving the Inequality

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To solve the inequality $7x > 77$, we need to isolate the variable $x$. We can do this by dividing both sides of the inequality by $7$. However, when dividing or multiplying an inequality by a negative number, we need to reverse the direction of the inequality sign.

7x > 77
x > 77/7
x > 11

Analyzing the Options

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Now that we have solved the inequality, let's analyze the given options:

A. $x \geq 77$ B. $x > 77$ C. $x < 11$ D. $x > 11$

Evaluating Option A

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Option A states that $x \geq 77$. However, our solution shows that $x > 11$, which is not equal to $77$. Therefore, option A is not the correct solution.

Evaluating Option B

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Option B states that $x > 77$. However, our solution shows that $x > 11$, which is not greater than $77$. Therefore, option B is not the correct solution.

Evaluating Option C

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Option C states that $x < 11$. However, our solution shows that $x > 11$, which is not less than $11$. Therefore, option C is not the correct solution.

Evaluating Option D

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Option D states that $x > 11$. Our solution shows that $x > 11$, which matches this option. Therefore, option D is the correct solution.

Conclusion

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In conclusion, the correct solution to the inequality $7x > 77$ is option D, which states that $x > 11$. This solution is obtained by dividing both sides of the inequality by $7$ and reversing the direction of the inequality sign when dividing by a negative number. Understanding inequalities and solving them is essential in mathematics, and this article provides a step-by-step guide on how to solve the given inequality.

Frequently Asked Questions

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Q: What is an inequality in mathematics?

A: An inequality is a statement that compares two or more values using a mathematical symbol, such as greater than ($>$), less than ($<$), greater than or equal to ($\geq$), or less than or equal to ($\leq$).

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. When dividing or multiplying an inequality by a negative number, you need to reverse the direction of the inequality sign.

Q: What is the correct solution to the inequality $7x > 77$?

A: The correct solution to the inequality $7x > 77$ is option D, which states that $x > 11$.

Final Thoughts

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Solving inequalities is an essential skill in mathematics, and it requires a deep understanding of the concept. By following the steps outlined in this article, you can solve inequalities with confidence. Remember to isolate the variable, reverse the direction of the inequality sign when dividing by a negative number, and analyze the options carefully to determine the correct solution.

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Introduction

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In our previous article, we discussed how to solve the inequality $7x > 77$ and determined the correct solution among the given options. In this article, we will provide a comprehensive Q&A guide on inequalities, covering various topics and concepts related to solving inequalities.

Q&A Section

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Q: What is an inequality in mathematics?

A: An inequality is a statement that compares two or more values using a mathematical symbol, such as greater than ($>$), less than ($<$), greater than or equal to ($\geq$), or less than or equal to ($\leq$).

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. When dividing or multiplying an inequality by a negative number, you need to reverse the direction of the inequality sign.

Q: What is the difference between an inequality and an equation?

A: An equation is a statement that says two values are equal, while an inequality is a statement that compares two or more values using a mathematical symbol.

Q: How do I determine the direction of the inequality sign?

A: When dividing or multiplying an inequality by a negative number, you need to reverse the direction of the inequality sign. For example, if you have the inequality $x > 5$ and you multiply both sides by $-2$, the inequality sign would change to $\leq$.

Q: Can I add or subtract the same value to both sides of an inequality?

A: Yes, you can add or subtract the same value to both sides of an inequality without changing the direction of the inequality sign. For example, if you have the inequality $x > 5$ and you add $3$ to both sides, the inequality would become $x + 3 > 8$.

Q: Can I multiply or divide both sides of an inequality by the same value?

A: Yes, you can multiply or divide both sides of an inequality by the same value without changing the direction of the inequality sign. For example, if you have the inequality $x > 5$ and you multiply both sides by $2$, the inequality would become $2x > 10$.

Q: What is the correct solution to the inequality $7x > 77$?

A: The correct solution to the inequality $7x > 77$ is option D, which states that $x > 11$.

Q: How do I solve a compound inequality?

A: A compound inequality is an inequality that contains two or more inequalities joined by the word "and" or "or". To solve a compound inequality, you need to solve each inequality separately and then combine the solutions.

Q: Can I use the same method to solve a compound inequality as I would for a single inequality?

A: No, you cannot use the same method to solve a compound inequality as you would for a single inequality. You need to solve each inequality separately and then combine the solutions.

Q: What is the difference between a linear inequality and a nonlinear inequality?

A: A linear inequality is an inequality that can be written in the form $ax + b > c$ or $ax + b < c$, where $a$, $b$, and $c$ are constants. A nonlinear inequality is an inequality that cannot be written in this form.

Q: How do I solve a nonlinear inequality?

A: To solve a nonlinear inequality, you need to use a different method, such as graphing or using a calculator.

Conclusion

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In conclusion, solving inequalities is an essential skill in mathematics, and it requires a deep understanding of the concept. By following the steps outlined in this article and using the Q&A guide, you can solve inequalities with confidence. Remember to isolate the variable, reverse the direction of the inequality sign when dividing by a negative number, and analyze the options carefully to determine the correct solution.

Final Thoughts

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Solving inequalities is an essential skill in mathematics, and it requires a deep understanding of the concept. By following the steps outlined in this article and using the Q&A guide, you can solve inequalities with confidence. Remember to isolate the variable, reverse the direction of the inequality sign when dividing by a negative number, and analyze the options carefully to determine the correct solution.

Additional Resources

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• Inequality Solutions: A Comprehensive Guide
• Mathematics for Dummies: Inequalities
• Inequality Solver: A Free Online Tool

Frequently Asked Questions

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Q: What is an inequality in mathematics?

A: An inequality is a statement that compares two or more values using a mathematical symbol, such as greater than ($>$), less than ($<$), greater than or equal to ($\geq$), or less than or equal to ($\leq$).

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. When dividing or multiplying an inequality by a negative number, you need to reverse the direction of the inequality sign.

Q: What is the correct solution to the inequality $7x > 77$?

A: The correct solution to the inequality $7x > 77$ is option D, which states that $x > 11$.

Final Answer

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The final answer is option D, which states that $x > 11$.