Question 24

x = 1/6

To solve the equation 9/(2x) = 27, we can first cross-multiply to obtain 9 = 54x. By isolating x, we find that x = 1/6.

A) x = 6

This option is incorrect because substituting x = 6 into the original equation results in 9/(2*6) = 9/12, which simplifies to 3/4, not equal to 27.

B) x = 27/9

This option simplifies to x = 3. However, substituting x = 3 into the original equation gives 9/(2*3) = 9/6, which simplifies to 3/2, not equal to 27.

C) x = 1/6

This option is correct. Substituting x = 1/6 into the original equation yields 9/(2*(1/6)) = 9/(1/3) = 27, confirming that this value satisfies the equation.

D) x = 54

This option is incorrect because substituting x = 54 into the original equation results in 9/(2*54) = 9/108, which simplifies to 1/12, not equal to 27.

Conclusion

The correct answer is x = 1/6, as it satisfies the original equation when substituted back. All other options fail to satisfy the equation, demonstrating a misunderstanding of how to manipulate the fractions involved. This reinforces the importance of accurately solving equations and understanding the relationships between the variables.