What Is The Solution Set Of $|-x|=-10$?A. $\{10\}$B. \$\{-10\}$[/tex\]C. $\{-10,10\}$D. No Solution

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Understanding Absolute Value Equations

Absolute value equations are a type of mathematical equation that involves the absolute value of a variable or expression. The absolute value of a number is its distance from zero on the number line, without considering direction. In other words, it is the magnitude of the number. When dealing with absolute value equations, we need to consider both the positive and negative possibilities of the variable or expression inside the absolute value bars.

The Equation $|-x|=-10$

The given equation is $|-x|=-10$. To solve this equation, we need to consider the definition of absolute value. The absolute value of a number is always non-negative, i.e., it is always greater than or equal to zero. Therefore, the equation $|-x|=-10$ is inconsistent, as the absolute value of a number cannot be negative.

Solution Set

Since the equation $|-x|=-10$ is inconsistent, it has no solution. In other words, there is no value of x that satisfies this equation. Therefore, the correct answer is:

No Solution

The solution set of the equation $|-x|=-10$ is the empty set, denoted by $\emptyset$. This means that there is no value of x that satisfies this equation.

Conclusion

In conclusion, the equation $|-x|=-10$ has no solution. This is because the absolute value of a number is always non-negative, and therefore, the equation is inconsistent. The correct answer is D. no solution.

Frequently Asked Questions

  • What is the solution set of the equation $|-x|=-10$?
  • The solution set of the equation $|-x|=-10$ is the empty set, denoted by $\emptyset$.
  • Why is the equation $|-x|=-10$ inconsistent?
  • The equation $|-x|=-10$ is inconsistent because the absolute value of a number is always non-negative.

Final Answer

The final answer is D. no solution.

Understanding Absolute Value Equations

Absolute value equations are a type of mathematical equation that involves the absolute value of a variable or expression. The absolute value of a number is its distance from zero on the number line, without considering direction. In other words, it is the magnitude of the number. When dealing with absolute value equations, we need to consider both the positive and negative possibilities of the variable or expression inside the absolute value bars.

The Equation $|-x|=-10$

The given equation is $|-x|=-10$. To solve this equation, we need to consider the definition of absolute value. The absolute value of a number is always non-negative, i.e., it is always greater than or equal to zero. Therefore, the equation $|-x|=-10$ is inconsistent, as the absolute value of a number cannot be negative.

Solution Set

Since the equation $|-x|=-10$ is inconsistent, it has no solution. In other words, there is no value of x that satisfies this equation. Therefore, the correct answer is:

No Solution

The solution set of the equation $|-x|=-10$ is the empty set, denoted by $\emptyset$. This means that there is no value of x that satisfies this equation.

Q&A

Q: What is the solution set of the equation $|-x|=-10$?

A: The solution set of the equation $|-x|=-10$ is the empty set, denoted by $\emptyset$.

Q: Why is the equation $|-x|=-10$ inconsistent?

A: The equation $|-x|=-10$ is inconsistent because the absolute value of a number is always non-negative.

Q: What is the definition of absolute value?

A: The absolute value of a number is its distance from zero on the number line, without considering direction. In other words, it is the magnitude of the number.

Q: Can the absolute value of a number be negative?

A: No, the absolute value of a number cannot be negative. It is always non-negative.

Q: What is the correct answer to the equation $|-x|=-10$?

A: The correct answer to the equation $|-x|=-10$ is D. no solution.

Q: Why is the equation $|-x|=-10$ not solvable?

A: The equation $|-x|=-10$ is not solvable because it is inconsistent. The absolute value of a number cannot be negative.

Q: What is the solution set of the equation $|-x|=-10$ in interval notation?

A: The solution set of the equation $|-x|=-10$ in interval notation is $\emptyset$.

Q: Can the equation $|-x|=-10$ be solved using algebraic methods?

A: No, the equation $|-x|=-10$ cannot be solved using algebraic methods. It is inconsistent and has no solution.

Conclusion

In conclusion, the equation $|-x|=-10$ has no solution. This is because the absolute value of a number is always non-negative, and therefore, the equation is inconsistent. The correct answer is D. no solution.

Final Answer

The final answer is D. no solution.

Frequently Asked Questions

  • What is the solution set of the equation $|-x|=-10$?
  • The solution set of the equation $|-x|=-10$ is the empty set, denoted by $\emptyset$.
  • Why is the equation $|-x|=-10$ inconsistent?
  • The equation $|-x|=-10$ is inconsistent because the absolute value of a number is always non-negative.
  • Can the absolute value of a number be negative?
  • No, the absolute value of a number cannot be negative. It is always non-negative.
  • What is the correct answer to the equation $|-x|=-10$?
  • The correct answer to the equation $|-x|=-10$ is D. no solution.
  • Why is the equation $|-x|=-10$ not solvable?
  • The equation $|-x|=-10$ is not solvable because it is inconsistent. The absolute value of a number cannot be negative.
  • What is the solution set of the equation $|-x|=-10$ in interval notation?
  • The solution set of the equation $|-x|=-10$ in interval notation is $\emptyset$.
  • Can the equation $|-x|=-10$ be solved using algebraic methods?
  • No, the equation $|-x|=-10$ cannot be solved using algebraic methods. It is inconsistent and has no solution.