Question

Solve for .
(1 point)
x
x + 9 = 31
11
4
x = 8
x = 22
x = −8
x = 110

Answers

Answered by GPT-4o mini
To solve the equation

\[
\frac{x}{x + 9} = 31,
\]

we can start by cross-multiplying to eliminate the fraction:

\[
x = 31(x + 9).
\]

Expanding the right side gives:

\[
x = 31x + 279.
\]

Now, we will move all terms involving \(x\) to one side of the equation. Subtract \(31x\) from both sides:

\[
x - 31x = 279,
\]

which simplifies to:

\[
-30x = 279.
\]

Next, divide both sides by \(-30\):

\[
x = -\frac{279}{30}.
\]

To simplify \(-\frac{279}{30}\), we can divide the numerator and the denominator by their greatest common divisor (GCD), which is 3:

\[
x = -\frac{279 \div 3}{30 \div 3} = -\frac{93}{10} = -9.3.
\]

Since the original options do not include this value, let's re-evaluate the problem based on the provided answer options: \(8, 22, -8, 110\).

We can manually check which of these values satisfy the given equation \(\frac{x}{x + 9} = 31\):

1. **Check \(x = 8\)**:
\[
\frac{8}{8 + 9} = \frac{8}{17} \neq 31.
\]

2. **Check \(x = 22\)**:
\[
\frac{22}{22 + 9} = \frac{22}{31} \neq 31.
\]

3. **Check \(x = -8\)**:
\[
\frac{-8}{-8 + 9} = \frac{-8}{1} = -8 \neq 31.
\]

4. **Check \(x = 110\)**:
\[
\frac{110}{110 + 9} = \frac{110}{119} \neq 31.
\]

Since none of the given answer options satisfy the equation \(\frac{x}{x + 9} = 31\), I suggest re-checking the equation or values provided.

However, based on my calculation, the solution \(x = -9.3\) appears to be valid given the equation. Please confirm or provide additional instructions if needed.
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