Question 16

X equals 6

To solve for X in the equation X/4 = 9/X, we can cross-multiply, resulting in X^2 = 36. Taking the square root of both sides gives us X = 6.

A) 6

Option A is correct because substituting X = 6 back into the original equation results in 6/4 = 9/6, which simplifies to 1.5 = 1.5, confirming that X = 6 satisfies the equation.

B) 8

Option B is incorrect. If we substitute X = 8 into the equation, we get 8/4 = 9/8, which simplifies to 2 = 1.125. This does not hold true, indicating that X = 8 is not a solution.

C) 12

Option C is also incorrect. Substituting X = 12 into the equation results in 12/4 = 9/12, simplifying to 3 = 0.75, which is false. Therefore, X = 12 does not satisfy the original equation.

D) 18

Option D is incorrect as well. When substituting X = 18, we have 18/4 = 9/18, which simplifies to 4.5 = 0.5. This statement is false, confirming that X = 18 is not a valid solution.

Conclusion

The solution to the equation X/4 = 9/X is X = 6, as it is the only option that satisfies the original equation upon substitution. All other options fail to maintain equality when substituted back into the equation, validating that they are incorrect. Thus, Option A is definitively the correct answer.