To find the solution for [tex]\( x \)[/tex] in the given equation [tex]\( 29 + 15x = -x - 3 \)[/tex], let's follow these steps:
1. Combine like terms involving [tex]\( x \)[/tex]:
Start by adding [tex]\( x \)[/tex] to both sides of the equation to simplify the terms with [tex]\( x \)[/tex]:
[tex]\[
29 + 15x + x = -x - 3 + x
\][/tex]
This simplifies to:
[tex]\[
29 + 16x = -3
\][/tex]
2. Isolate the term with [tex]\( x \)[/tex]:
Next, subtract 29 from both sides to isolate the [tex]\( x \)[/tex] term:
[tex]\[
29 + 16x - 29 = -3 - 29
\][/tex]
This simplifies to:
[tex]\[
16x = -32
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 16 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-32}{16}
\][/tex]
This simplifies to:
[tex]\[
x = -2
\][/tex]
The solution for [tex]\( x \)[/tex] is [tex]\( \boxed{-2} \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -2 \)[/tex]
