To solve the equation [tex]\( 29 + 15x = -x - 3 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Combine like terms involving [tex]\( x \)[/tex]:
[tex]\[
29 + 15x = -x - 3
\][/tex]
Add [tex]\( x \)[/tex] to both sides to combine the terms involving [tex]\( x \)[/tex]:
[tex]\[
29 + 15x + x = -x - 3 + x
\][/tex]
Simplifying this:
[tex]\[
29 + 16x = -3
\][/tex]
2. Isolate the [tex]\( x \)[/tex]-term:
Subtract 29 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
29 + 16x - 29 = -3 - 29
\][/tex]
Simplifying this:
[tex]\[
16x = -32
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], divide both sides by 16:
[tex]\[
x = \frac{-32}{16}
\][/tex]
Simplifying the fraction:
[tex]\[
x = -2
\][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( -2 \)[/tex].
Looking at the answer choices:
- A. [tex]\( x = -\frac{1}{2} \)[/tex]
- B. [tex]\( x = -2 \)[/tex]
- C. [tex]\( x = 2 \)[/tex]
- D. [tex]\( x = \frac{1}{2} \)[/tex]
The correct answer is:
[tex]\[
\boxed{B}
\][/tex]
