Sure, let's solve the equation step-by-step.
The given equation is:
[tex]\[ -12x - 2(x + 9) = 5(x + 4) \][/tex]
First, let's simplify each side of the equation.
Distribute the [tex]\(-2\)[/tex] on the left-hand side:
[tex]\[ -12x - 2(x + 9) = -12x - 2x - 18 \][/tex]
Combine like terms on the left-hand side:
[tex]\[ -12x - 2x - 18 = -14x - 18 \][/tex]
Next, distribute the [tex]\(5\)[/tex] on the right-hand side:
[tex]\[ 5(x + 4) = 5x + 20 \][/tex]
Our equation now looks like this:
[tex]\[ -14x - 18 = 5x + 20 \][/tex]
To isolate [tex]\(x\)[/tex], we need to get all [tex]\(x\)[/tex]-terms on one side and constant terms on the other side. Start by adding [tex]\(14x\)[/tex] to both sides:
[tex]\[ -14x + 14x - 18 = 5x + 14x + 20 \][/tex]
[tex]\[ -18 = 19x + 20 \][/tex]
Now, subtract [tex]\(20\)[/tex] from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -18 - 20 = 19x + 20 - 20 \][/tex]
[tex]\[ -38 = 19x \][/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(19\)[/tex]:
[tex]\[ x = \frac{-38}{19} \][/tex]
[tex]\[ x = -2 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] that makes the equation true is [tex]\(\boxed{-2}\)[/tex].
So the correct answer is:
A. -2
