To determine the number of solutions for the given equation:
[tex]\[
9x - 16 = 9x - 23
\][/tex]
we will follow these steps:
1. Isolate the variable [tex]\( x \)[/tex]:
Begin by subtracting [tex]\( 9x \)[/tex] from both sides of the equation to eliminate the [tex]\( 9x \)[/tex] terms:
[tex]\[
9x - 16 - 9x = 9x - 23 - 9x
\][/tex]
2. Simplify the equation:
This simplifies to:
[tex]\[
-16 = -23
\][/tex]
3. Analyze the simplification:
Notice that the resulting equation [tex]\(-16 = -23\)[/tex] is a contradiction. This means that the left-hand side (LHS) is not equal to the right-hand side (RHS), no matter the value of [tex]\( x \)[/tex].
Since we encounter a contradiction, it indicates that there are no values of [tex]\( x \)[/tex] that can satisfy the original equation.
Therefore, the number of solutions to the equation [tex]\( 9x - 16 = 9x - 23 \)[/tex] is:
[tex]\[
\boxed{0}
\][/tex]
