Question

Rewrite the equation $32=-25+\frac {9-x}{x+7}$ as two equations joined by "and."
$32=-25+\frac {9-x}{x+7}$ and $x\neq -9$
$32=-25+\frac {9-x}{x+7}$ and $x\neq -7$
$32=-25+\frac {9-x}{x+7}$ and $x\neq 7$
$32=-25+\frac {9-x}{x+7}$ and $x\neq 9$

Answer 1

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:
\[
32 = -25 + \frac{9 - x}{x + 7} \quad \text{and} \quad x \neq -7
\]