What Is The Value Of $x$ In The Equation $-\frac{6}{7} = -\frac{x}{84}$?A. $-98$B. $-72$C. $72$D. $98$

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Understanding the Equation

The given equation is $-\frac{6}{7} = -\frac{x}{84}$. To find the value of $x$, we need to isolate $x$ on one side of the equation. This can be done by multiplying both sides of the equation by the reciprocal of the coefficient of $x$, which is $-\frac{84}{-1}$.

Solving for $x$

To solve for $x$, we can start by multiplying both sides of the equation by $-\frac{84}{-1}$.

$$-\frac{6}{7} \cdot -\frac{84}{-1} = -\frac{x}{84} \cdot -\frac{84}{-1}$$

This simplifies to:

$$\frac{6 \cdot 84}{7 \cdot -1} = \frac{x \cdot 84}{84 \cdot -1}$$

$$\frac{504}{-7} = \frac{84x}{-84}$$

Simplifying the Equation

Now, we can simplify the equation by dividing both sides by $-84$.

$$\frac{504}{-7} \div -84 = \frac{84x}{-84} \div -84$$

This simplifies to:

$$\frac{504}{-7} \cdot \frac{1}{-84} = \frac{84x}{-84} \cdot \frac{1}{-84}$$

$$\frac{504}{-7 \cdot 84} = \frac{84x}{-84 \cdot -84}$$

$$\frac{504}{-588} = \frac{84x}{7056}$$

Finding the Value of $x$

Now, we can find the value of $x$ by multiplying both sides of the equation by $7056$.

$$\frac{504}{-588} \cdot 7056 = \frac{84x}{7056} \cdot 7056$$

This simplifies to:

$$\frac{504 \cdot 7056}{-588} = \frac{84x \cdot 7056}{7056}$$

$$\frac{3547776}{-588} = 84x$$

Calculating the Value of $x$

Now, we can calculate the value of $x$ by dividing both sides of the equation by $84$.

$$\frac{3547776}{-588} \div 84 = 84x \div 84$$

This simplifies to:

$$\frac{3547776}{-588} \cdot \frac{1}{84} = 84x \cdot \frac{1}{84}$$

$$\frac{3547776}{-588 \cdot 84} = x$$

$$\frac{3547776}{-49392} = x$$

Final Answer

The final answer is:

$$x = -72$$

This is the value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$.

Conclusion

In this article, we have shown how to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$. We started by multiplying both sides of the equation by the reciprocal of the coefficient of $x$, which is $-\frac{84}{-1}$. We then simplified the equation by dividing both sides by $-84$. Finally, we calculated the value of $x$ by dividing both sides of the equation by $84$. The final answer is $x = -72$.

Frequently Asked Questions

• What is the value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?
• How do I solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?
• What is the reciprocal of the coefficient of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

Answer to Frequently Asked Questions

• The value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$ is $-72$.
• To solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$, you need to multiply both sides of the equation by the reciprocal of the coefficient of $x$, which is $-\frac{84}{-1}$.
• The reciprocal of the coefficient of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$ is $-\frac{84}{-1}$.

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra and Its Applications" by Gilbert Strang
• [3] "Calculus" by Michael Spivak

Note: The references provided are for general information and are not specific to the equation $-\frac{6}{7} = -\frac{x}{84}$.

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Frequently Asked Questions

Q: What is the value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: The value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$ is $-72$.

Q: How do I solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: To solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$, you need to multiply both sides of the equation by the reciprocal of the coefficient of $x$, which is $-\frac{84}{-1}$.

Q: What is the reciprocal of the coefficient of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: The reciprocal of the coefficient of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$ is $-\frac{84}{-1}$.

Q: Can I use a calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: Yes, you can use a calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$. Simply enter the equation into the calculator and press the "solve" button.

Q: What if I get a different answer when using a calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: If you get a different answer when using a calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$, it may be due to a calculation error or a mistake in the equation. Double-check your work and make sure you are using the correct equation.

Q: Can I use a graphing calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: Yes, you can use a graphing calculator to solve for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$. Simply enter the equation into the calculator and use the "solve" function to find the value of $x$.

Q: What if I am having trouble solving for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$?

A: If you are having trouble solving for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$, try breaking down the problem into smaller steps. You can also try using a different method, such as using a calculator or a graphing calculator.

Additional Resources

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra and Its Applications" by Gilbert Strang
• [3] "Calculus" by Michael Spivak

Note: The references provided are for general information and are not specific to the equation $-\frac{6}{7} = -\frac{x}{84}$.

Conclusion

In this article, we have provided answers to frequently asked questions about solving for $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$. We have also provided additional resources for further learning. If you have any further questions or need additional help, please don't hesitate to ask.

Final Answer

The final answer is:

$$x = -72$$

This is the value of $x$ in the equation $-\frac{6}{7} = -\frac{x}{84}$.