https://file.aiquickdraw.com/mathbot/file/17254673291486e8j0r74.jpg

The equation in the image is:

\[
\left| \frac{x - 5}{5 - x} \right| = \frac{6}{5 - x} - 5
\]

Let's solve this step by step.

### Step 1: Simplify the equation
The left side of the equation can be simplified by recognizing that:

\[
\left| \frac{x - 5}{5 - x} \right| = \left| \frac{-(5 - x)}{5 - x} \right| = \left| -1 \right| = 1
\]

So, the equation simplifies to:

\[
1 = \frac{6}{5 - x} - 5
\]

### Step 2: Solve for \( x \)
Add 5 to both sides:

\[
1 + 5 = \frac{6}{5 - x}
\]

Simplify the left side:

\[
6 = \frac{6}{5 - x}
\]

### Step 3: Clear the fraction
To solve the equation, multiply both sides by \( 5 - x \):

\[
6(5 - x) = 6
\]

Distribute the 6 on the left side:

\[
30 - 6x = 6
\]

### Step 4: Isolate \( x \)
Subtract 30 from both sides:

\[
-6x = 6 - 30
\]

Simplify the right side:

\[
-6x = -24
\]

Finally, divide by -6:

\[
x = 4
\]

### Conclusion
The solution to the equation is \( x = 4 \).

---

Would you like more details or have any questions about the solution?

Here are 5 additional questions related to the problem:

1. What are some common properties of absolute values that are useful in solving equations?
2. How would the solution change if the absolute value in the equation were different?
3. Can you solve a similar equation where the fraction and absolute value involve different expressions?
4. What happens if you encounter an equation where the absolute value expression equals a negative number?
5. How can you check if the solution to the equation is correct?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure that both sides are equal.

Los vervolgens op vir x: |x - 5| / (5 - x) = 6 / (5 - x) - 5

Step-by-step guide to solving a rational equation involving absolute values. Explore the key concepts and algebraic manipulations required for solving such equations, suitable for students in Grades 9-10.

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