To rewrite the equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we start by simplifying the original equation.
First, combine terms on the left side:
\[ \frac{5}{2}x - 9 = 9 \]
Now, to isolate \( \frac{5}{2}x \):
\[ \frac{5}{2}x = 9 + 9 \] \[ \frac{5}{2}x = 18 \]
Next, we multiply both sides by \( \frac{2}{5} \):
\[ x = \frac{2}{5} \cdot 18 \] \[ x = \frac{36}{5} \]
Now, if we want to express this in the form of two equations joined by "and," we have:
\[ \frac{5}{2}x - 8 - 1 = 9 \quad \text{and} \quad x \neq -8 \]
However, we need to find the relation to the other options. Since the equation will not restrict \( x \) to any particular value such as 4 or -4, and we derived that \( x \) can equal \( \frac{36}{5} \) given the equation's structure.
After analyzing the options:
- Option (a) does not apply, as it implies \( x \) cannot equal -8, which is irrelevant here.
- Option (b) suggests other conditions which don’t match.
- Option (c) suggests restrictions based on an incorrect interpretation.
- Option (d) suggests a restriction that cannot be applied.
Given these considerations, based on standard interpretations, the best fit from the list you provided is:
b. \(\frac{5}{2}x - 8 - 1 = 9\) and \( x \neq 8\).
However, ideally, an exact representation should avoid stating conditions unless necessary, as no zeroing or undefined values emerge directly from the equation itself beyond variable solution contexts.
So, based on the provided context, one correct statement could be that:
Answer: a. \(\frac{5}{2}x - 8 = 9\) and \( x \neq -8\).