To determine how many solutions the equation has, let's simplify and analyze it step-by-step.
First, consider the initial equation:
[tex]\[ 9z - 6 + 7z = 16z - 6 \][/tex]
Combine like terms on the left side:
[tex]\[ 9z + 7z - 6 = 16z - 6 \][/tex]
[tex]\[ 16z - 6 = 16z - 6 \][/tex]
Now, observe that both sides of the equation are identical. This implies that the equation holds true for any value of [tex]\( z \)[/tex]. Therefore, the equation is an identity.
When an equation simplifies to an identity (a true statement regardless of the variable), it indicates that there are infinitely many solutions.
Thus, the number of solutions is:
(C) Infinitely many solutions
