Final answer:
The simplified expression for ({6}{x-6} - {5}{12x-4}) is -54x - 16.
None of the given options is correct
Step-by-step explanation:
To solve the expression ({6}{x-6} - {5}{12x-4}), we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
1. First, let's simplify the expression inside the parentheses.
Inside the first set of parentheses, {6}{x-6}, we have a coefficient of 6 and a binomial (x-6). To simplify this, we distribute the 6 to each term in the binomial:
{6(x) - 6(6)} = 6x - 36.
Inside the second set of parentheses, {5}{12x-4}, we have a coefficient of 5 and a binomial (12x-4). To simplify this, we distribute the 5 to each term in the binomial:
{5(12x) - 5(4)} = 60x - 20.
2. Now, let's substitute the simplified expressions back into the original expression:
6x - 36 - (60x - 20).
3. Next, let's simplify further by distributing the negative sign to each term inside the parentheses:
6x - 36 - 60x + 20.
4. Now, let's combine like terms:
(6x - 60x) + (-36 + 20) = -54x - 16.
Therefore, the simplified expression for ({6}{x-6} - {5}{12x-4}) is -54x - 16.
None of the answer choices provided match the simplified expression, so the correct answer is none of the above.