To solve the equation [tex]\(-3x + 7x - 8 = 34 + 9x - 2\)[/tex], follow these steps:
1. Combine like terms on each side of the equation:
[tex]\[
(-3x + 7x) - 8 = (34 - 2) + 9x
\][/tex]
Simplifying within the parentheses:
[tex]\[
4x - 8 = 32 + 9x
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the equation and constant terms to the other side:
Subtract [tex]\(9x\)[/tex] from both sides to start isolating [tex]\(x\)[/tex]:
[tex]\[
4x - 9x - 8 = 32
\][/tex]
Simplifying the [tex]\(x\)[/tex]-terms:
[tex]\[
-5x - 8 = 32
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term by adding 8 to both sides:
[tex]\[
-5x = 32 + 8
\][/tex]
Simplifying the constants:
[tex]\[
-5x = 40
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by -5:
[tex]\[
x = \frac{40}{-5}
\][/tex]
[tex]\[
x = -8
\][/tex]
Therefore, the solution is:
[tex]\(\boxed{-8}\)[/tex]
The correct answer is:
C. [tex]\( x = -8 \)[/tex]
