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The problem given is:

"If the fraction \(\frac{396}{x - 10}\) is equivalent to \(-22\), find the value of \(x\). Show your work."

### Solution:

We are given the equation:
\[
\frac{396}{x - 10} = -22
\]

To solve for \(x\), follow these steps:

1. **Multiply both sides by \((x - 10)\)** to eliminate the fraction:
   \[
   396 = -22(x - 10)
   \]

2. **Distribute \(-22\) on the right-hand side**:
   \[
   396 = -22x + 220
   \]

3. **Move the constant term \(220\) to the left-hand side** by subtracting \(220\) from both sides:
   \[
   396 - 220 = -22x
   \]
   Simplifying:
   \[
   176 = -22x
   \]

4. **Solve for \(x\)** by dividing both sides by \(-22\):
   \[
   x = \frac{176}{-22} = -8
   \]

### Final Answer:
\[
x = -8
\]

Would you like more details on the steps or have any questions?

Here are 5 related questions for further practice:

1. Solve for \(x\): \(\frac{500}{x - 15} = -25\).
2. Find \(x\) if \(\frac{120}{x + 5} = 15\).
3. Solve for \(y\) if \(\frac{y}{x - 4} = 3\) and \(x = 8\).
4. Solve the equation \(\frac{700}{x + 20} = 50\) for \(x\).
5. Find \(x\) if \(\frac{350}{x - 2} = -50\).

**Tip:** When solving fractional equations, always check for potential restrictions, like division by zero, which would make the equation undefined.

If the fraction 396/(x - 10) is equivalent to -22, find the value of x. Show your work.

Learn how to solve the equation 396/(x - 10) = -22 with step-by-step explanations. This problem involves basic algebraic concepts like fractions and linear equations. Suitable for students in Grades 8-10.

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