Sure! Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex] that makes the equation true:
[tex]\[
-12x - 2(x + 9) = 5(x + 4)
\][/tex]
1. Distribute the constants on both sides:
[tex]\[
-12x - 2x - 18 = 5x + 20
\][/tex]
2. Combine like terms on the left side:
[tex]\[
-14x - 18 = 5x + 20
\][/tex]
3. Add 14x to both sides to move all the terms involving [tex]\( x \)[/tex] to one side:
[tex]\[
-18 = 19x + 20
\][/tex]
4. Subtract 20 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-18 - 20 = 19x
\][/tex]
[tex]\[
-38 = 19x
\][/tex]
5. Divide by 19 on both sides 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]
Therefore, the correct answer is:
B. -2
