Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex]:
The given equation is:
[tex]\[
-3x + 7x - 8 = 34 + 9x - 2
\][/tex]
First, we simplify both sides of the equation.
On the left side:
[tex]\[
-3x + 7x - 8 = 4x - 8
\][/tex]
On the right side:
[tex]\[
34 + 9x - 2 = 9x + 32
\][/tex]
Now, we have the equation:
[tex]\[
4x - 8 = 9x + 32
\][/tex]
Next, we need to get all the terms involving [tex]\( x \)[/tex] on one side and the constant terms on the other side. Subtract [tex]\( 9x \)[/tex] from both sides:
[tex]\[
4x - 9x - 8 = 32
\][/tex]
This simplifies to:
[tex]\[
-5x - 8 = 32
\][/tex]
Next, add 8 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-5x = 32 + 8
\][/tex]
This simplifies to:
[tex]\[
-5x = 40
\][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by -5:
[tex]\[
x = \frac{40}{-5} = -8
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = -8
\][/tex]
The correct answer is:
[tex]\[
\boxed{B. \, x = -8}
\][/tex]
