To solve the equation \( 6z - 3z - 7 = -2 + 3 \), we can start by simplifying both sides.
First, simplify the left-hand side:
\[ 6z - 3z - 7 = 3z - 7 \]
Now, simplify the right-hand side:
\[ -2 + 3 = 1 \]
Thus, we can rewrite the equation as:
\[ 3z - 7 = 1 \]
Next, add 7 to both sides to isolate the term with \( z \):
\[ 3z = 1 + 7 \] \[ 3z = 8 \]
Now, divide both sides by 3:
\[ z = \frac{8}{3} \]
Since we found a specific value for \( z \), this indicates that there is exactly one solution to the equation.
Therefore, the answer is One.