Let's solve the equation step-by-step:
The given equation is:
[tex]\[
-12x - 2(x + 9) = 5(x + 4)
\][/tex]
First, we need to distribute the terms inside the parentheses:
[tex]\[
-12x - 2(x + 9) = 5(x + 4)
\][/tex]
[tex]\[
-12x - 2x - 18 = 5x + 20
\][/tex]
Next, combine the like terms on the left side of the equation:
[tex]\[
-14x - 18 = 5x + 20
\][/tex]
Now, we want to isolate [tex]\( x \)[/tex], so let's move all terms involving [tex]\( x \)[/tex] to one side and the constant terms to the other side. To do this, we add [tex]\( 14x \)[/tex] to both sides:
[tex]\[
-14x + 14x - 18 = 5x + 14x + 20
\][/tex]
[tex]\[
-18 = 19x + 20
\][/tex]
Next, subtract 20 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-18 - 20 = 19x
\][/tex]
[tex]\[
-38 = 19x
\][/tex]
Divide both sides by 19 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-38}{19}
\][/tex]
[tex]\[
x = -2
\][/tex]
So, the value of [tex]\( x \)[/tex] that makes the equation true is:
[tex]\[
\boxed{-2}
\][/tex]
Looking at the given options, the correct answer is:
A. -2
