To solve the equation [tex]\(-12x - 2(x + 9) = 5(x + 4)\)[/tex], let's follow these detailed steps:
1. Distribute the constants on both sides of the equation:
[tex]\[
-12x - 2(x + 9) = 5(x + 4)
\][/tex]
Distribute [tex]\(-2\)[/tex] on the left side:
[tex]\[
-12x - 2x - 18 = 5(x + 4)
\][/tex]
2. Simplify the left side:
Combine like terms:
[tex]\[
-14x - 18 = 5x + 20
\][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side:
Add [tex]\(14x\)[/tex] to both sides:
[tex]\[
-18 = 19x + 20
\][/tex]
Subtract 20 from both sides:
[tex]\[
-38 = 19x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 19:
[tex]\[
x = \frac{-38}{19}
\][/tex]
Simplify the fraction:
[tex]\[
x = -2
\][/tex]
After solving the equation, we find that [tex]\(x = -2\)[/tex].
Thus, the correct answer is:
A. -2
