Final answer:
Upon solving the equation 0.5(4x - 3) = 12x + 16.5 by algebraic rearrangement, we find that x = -1.8, which does not match any of the provided options.
Step-by-step explanation:
To solve the equation 0.5(4x - 3) = 12x + 16.5 for x, we need to apply algebraic rearrangement. First, distribute the 0.5 into the parentheses:
2x - 1.5 = 12x + 16.5
Next, move all terms involving x to one side and constant terms to the other:
2x - 12x = 16.5 + 1.5
Combine like terms:
-10x = 18
Finally, divide both sides by -10 to solve for x:
x = 18 / -10
x = -1.8
So the solution is not among the provided options, and there may have been a mistake in the question or answer choices.