To solve the equation [tex]\( 9(x + 4) + 6 = 9x + 8 \)[/tex], we need to simplify both sides and find the value of [tex]\( x \)[/tex].
First, distribute the 9 on the left side:
[tex]\[
9(x + 4) + 6 = 9x + 36 + 6
\][/tex]
This simplifies to:
[tex]\[
9x + 36 + 6 = 9x + 42
\][/tex]
Now, our equation looks like:
[tex]\[
9x + 42 = 9x + 8
\][/tex]
Next, subtract [tex]\( 9x \)[/tex] from both sides of the equation:
[tex]\[
9x + 42 - 9x = 9x + 8 - 9x
\][/tex]
This simplifies to:
[tex]\[
42 = 8
\][/tex]
Since 42 does not equal 8, we have a contradiction. Therefore, there is no value of [tex]\( x \)[/tex] that can satisfy the original equation.
Thus, the correct choice is:
C. There is no solution.
