To rewrite the equation \( 32 = -25 + 9 - \frac{x}{x} + 7 \) as two equations joined by "and," we first need to simplify the expression.
-
Simplifying the equation: \[ 32 = -25 + 9 - \frac{x}{x} + 7 \]
The term \( -\frac{x}{x} \) simplifies to \(-1\) (assuming \(x \neq 0\)).
Therefore, we have: \[ 32 = -25 + 9 - 1 + 7 \]
Now let's simplify: \[ 32 = -25 + 9 - 1 + 7 = -25 + 15 = -10 \]
-
This gives us the simplified equation: \[ 32 = -10 \] which is not true, thus there is no solution.
-
The restriction \(x \neq 0\) comes from the term \(-\frac{x}{x}\), so we also need to consider this when writing the final answer.
Putting this together, the equivalent representation of the original equation can be expressed as:
\[ 32 = -25 + 9 - \frac{x}{x} + 7 \text{ and } x \neq 0 \]
In a more appropriate format: \[ 32 = -25 + 9 - 1 + 7 \text{ and } x \neq 0 \]
If we assume we mean a form close to what's given in the options, and implying no solutions overall just because of contradictions, the correct rewritten statement with "and" could also specify that \(x \neq 0\) without contradicting simplification:
Thus we can conclude with: \[ 32 = -25 + 9 - \frac{x}{x} + 7 \text{ and } x \neq 0 \]
However, from the options provided, it looks as if you are trying to get a specific value to relate back to without contradiction. None of the provided option sets are correct since they imply something true but give ranges that either lead to contradictions in values or from what was simplified could lead us to conclude differently.
The correct response with all interpretations would be relates to: \[ 32 = -25 + 9 - \frac{x}{x} + 7 \text{ and } x \neq 0 \] is not one of them.
1 answer