To solve the equation [tex]\(-3x + 7x - 8 = 34 + 9x - 2\)[/tex], we will proceed with the following steps:
1. Simplify both sides of the equation.
\begin{align}
-3x + 7x - 8 &= 34 + 9x - 2
\end{align}
Combine like terms on both sides:
\begin{align}
(7x - 3x) - 8 &= 34 - 2 + 9x \\
4x - 8 &= 32 + 9x
\end{align}
2. Bring all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side.
\begin{align}
4x - 8 &= 32 + 9x
\end{align}
Subtract [tex]\(9x\)[/tex] from both sides:
\begin{align}
4x - 9x - 8 &= 32 \\
-5x - 8 &= 32
\end{align}
3. Isolate the [tex]\(x\)[/tex] term.
Add 8 to both sides:
\begin{align}
-5x &= 32 + 8 \\
-5x &= 40
\end{align}
Divide both sides by [tex]\(-5\)[/tex]:
\begin{align}
x &= \frac{40}{-5} \\
x &= -8
\end{align}
Hence, the solution for the equation [tex]\(-3x + 7x - 8 = 34 + 9x - 2\)[/tex] is [tex]\(x = -8\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{x = -8} \][/tex]
```option c```
