Solve The Equation For The Value Of { A $} : : : { \left(\frac{8}{5}\right)^2 = \frac{123}{7} \} Options:A. No Value Of { A $}$ Will Work.B. { A = 1 $}$C. { A = 2 $}$D. { A = 3 $}$

Introduction

In this article, we will be solving an equation to find the value of a variable 'a'. The equation given is $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$. We will go through the steps to solve this equation and find the correct value of 'a'.

Understanding the Equation

The given equation is $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$. To solve this equation, we need to first simplify the left-hand side by squaring the fraction $\frac{8}{5}$. This can be done by multiplying the numerator and denominator by themselves.

$\left(\frac{8}{5}\right)^2 = \frac{8^2}{5^2} = \frac{64}{25}$

Now, the equation becomes $\frac{64}{25} = \frac{123}{7}$.

Simplifying the Equation

To simplify the equation further, we can cross-multiply the fractions. This means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.

$64 \times 7 = 123 \times 25$

This gives us $448 = 3075$.

Analyzing the Result

However, we can see that the result $448 = 3075$ is not true. This means that the original equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ is not correct.

Conclusion

Since the original equation is not correct, we cannot find a value of 'a' that satisfies the equation. Therefore, the correct answer is:

No value of a will work

This means that none of the options A, B, C, or D are correct.

Why the Options are Incorrect

Let's analyze why the options A, B, C, and D are incorrect.

• Option A: No value of a will work. This is correct because the original equation is not true.
• Option B: a = 1. This is incorrect because we cannot find a value of 'a' that satisfies the equation.
• Option C: a = 2. This is also incorrect for the same reason as option B.
• Option D: a = 3. This is incorrect because we cannot find a value of 'a' that satisfies the equation.

Final Answer

The final answer is:

• No value of a will work.

This means that none of the options A, B, C, or D are correct.

Additional Information

If you are still unsure about the solution, you can try plugging in the values of 'a' from the options A, B, C, and D into the original equation to see if any of them work. However, as we have already seen, none of the options will work.

Conclusion

Q: What is the correct solution to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$?

A: The correct solution to the equation is that no value of 'a' will work. This means that none of the options A, B, C, or D are correct.

Q: Why is the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ not true?

A: The equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ is not true because the result of squaring the fraction $\frac{8}{5}$ is $\frac{64}{25}$, which is not equal to $\frac{123}{7}$.

Q: Can I find a value of 'a' that satisfies the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$?

A: No, you cannot find a value of 'a' that satisfies the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$. The equation is not true, and therefore, no value of 'a' will work.

Q: What is the difference between the options A, B, C, and D?

A: The options A, B, C, and D are all incorrect because they do not satisfy the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$. Option A states that no value of 'a' will work, which is correct. Options B, C, and D state that 'a' equals 1, 2, and 3, respectively, but these values do not satisfy the equation.

Q: Can I use the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ to solve for 'a'?

A: No, you cannot use the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ to solve for 'a'. The equation is not true, and therefore, it cannot be used to solve for 'a'.

Q: What is the final answer to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$?

A: The final answer to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ is that no value of 'a' will work. This means that none of the options A, B, C, or D are correct.

Q: Can I find a different solution to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$?

A: No, you cannot find a different solution to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$. The equation is not true, and therefore, there is no other solution.

Q: What is the main takeaway from this article?

A: The main takeaway from this article is that the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ is not true, and therefore, no value of 'a' will work. This means that none of the options A, B, C, or D are correct.

Conclusion

In conclusion, the correct answer to the equation $\left(\frac{8}{5}\right)^2 = \frac{123}{7}$ is that no value of 'a' will work. This means that none of the options A, B, C, or D are correct. We hope this article has helped you understand how to solve the equation and find the correct value of 'a'.