Final answer:
After simplifying the given equation, we find that for the equation to balance, m must equal -5/4 and b must equal -14. However, these values are not given in the options, indicating a possible error either in the equation provided or in the options listed.
Step-by-step explanation:
The equation -4(mx + 2) - (3x + 6) = 5x + b can be simplified to find the correct values of m and b that make the equation true. First, distribute the -4 into (mx + 2) and -1 into (3x + 6), resulting in -4mx - 8 - 3x - 6.
Next, combine like terms, resulting in -4mx - 3x - 8 - 6, which simplifies to -4mx - 3x - 14. Comparing this with the right side of the equation, 5x + b, for both sides to be equal -4m must be equal to 5 (the coefficient of x) and -14 should be equal to b (the constant term). For the equation to balance correctly, m = -5/4 and b = -14. However, these values are not included in the options provided, so it seems there is a mistake. None of the options (A, B, C, or D) will make the given equation true with the method used.