To rewrite the equation \( 32 = -25 + \frac{9 - x}{x + 7} \) as two equations joined by "and," we need to analyze the equation and identify any restrictions on \(x\).
Starting with the equation: \[ 32 = -25 + \frac{9 - x}{x + 7} \]
We can isolate the fraction: \[ 32 + 25 = \frac{9 - x}{x + 7} \] \[ 57 = \frac{9 - x}{x + 7} \]
Next, we multiply both sides by \(x + 7\) (noting that \(x + 7 \neq 0\) implies \(x \neq -7\)): \[ 57(x + 7) = 9 - x \]
Expanding the left side: \[ 57x + 399 = 9 - x \]
Next, we rearrange this to isolate \(x\): \[ 57x + x = 9 - 399 \] \[ 58x = -390 \] \[ x = -\frac{390}{58} = -\frac{195}{29} \]
Thus, we have the solution \(x = -\frac{195}{29}\), but we also need to account for the restriction that \(x \neq -7\) to avoid division by zero in the original equation.
Hence, the final result can be written as: \[ 32 = -25 + \frac{9 - x}{x + 7} \quad \text{and} \quad x \neq -7 \]
So, the final answer is: \[ 32 = -25 + \frac{9 - x}{x + 7} \quad \text{and} \quad x \neq -7 \]
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