To solve the equation [tex]\( 3x + 8 = x - 12 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Move all terms involving [tex]\( x \)[/tex] to one side of the equation:
Subtract [tex]\( x \)[/tex] from both sides to get:
[tex]\[
3x + 8 - x = x - 12 - x
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x + 8 = -12
\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
Subtract 8 from both sides to get:
[tex]\[
2x + 8 - 8 = -12 - 8
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x = -20
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2 to get:
[tex]\[
\frac{2x}{2} = \frac{-20}{2}
\][/tex]
Simplifying both sides, we get:
[tex]\[
x = -10
\][/tex]
Thus, the solution for [tex]\( x \)[/tex] is [tex]\(-10\)[/tex].
Therefore, the best answer is:
C. [tex]\(-10\)[/tex]
