To determine how many solutions the equation [tex]\( 9(x - 4) = 9x - 33 \)[/tex] has, we can follow a series of algebraic steps:
1. Simplify both sides of the equation:
- On the left side, distribute the [tex]\( 9 \)[/tex]:
[tex]\[
9(x - 4) = 9x - 36
\][/tex]
- The right side remains the same:
[tex]\[
9x - 33
\][/tex]
2. Set the simplified forms of both sides equal to each other:
[tex]\[
9x - 36 = 9x - 33
\][/tex]
3. Subtract [tex]\( 9x \)[/tex] from both sides to isolate constants:
[tex]\[
9x - 36 - 9x = 9x - 33 - 9x
\][/tex]
[tex]\[
-36 = -33
\][/tex]
4. Analyze the resulting statement:
[tex]\[
-36 = -33
\][/tex]
This statement is clearly false because [tex]\(-36\)[/tex] does not equal [tex]\(-33\)[/tex].
Since we have arrived at a false statement (an inconsistency), it means that there is no value of [tex]\( x \)[/tex] that can satisfy the original equation.
Conclusion:
There are no solutions to the equation [tex]\( 9(x - 4) = 9x - 33 \)[/tex]. The correct answer is:
A. 0
