Final answer:
Solving the given equation using cross multiplication and algebraic simplification leads to a quadratic equation that does not factor cleanly to match any of the given multiple-choice answers. The student may need to check for any errors in the provided equation or the algebraic steps taken.
Step-by-step explanation:
To solve the equation 4 / (7(x + 6)) = x / (x + 6), we need to find a common denominator. The common denominator here is already present, which is 7(x + 6). We can cross multiply to solve for x.
Multiplying the numerator of one fraction by the denominator of the other gives us:
4(x + 6) = 7(x + 6)x
Expanding both sides:
4x + 24 = 7x^2 + 42x
Bring all terms to one side to set the equation to zero:
7x^2 + 42x - 4x - 24 = 0
Simplify:
7x^2 + 38x - 24 = 0
This is a quadratic equation, which we can solve using factoring, completing the square, or the quadratic formula. Assuming none of these methods result in a solution that matches the provided options, it seems there might be a typo, or that this equation is not factorable to yield one of the multiple-choice answers provided.
Thus, without further simplification or factoring, we can note that the student needs to revisit the equation or the process again, possibly checking for initial input error or missteps in algebraic manipulation.