https://file.aiquickdraw.com/mathbot/file/1727178330740r7hn8gs2.jpg

Let's re-examine the inequality and solve it step-by-step to determine the correct set.

### Problem Statement
We need to find the solution set of the inequality:

\[
|6 - 5x| \leq 10
\]

### Step 1: Remove the Absolute Value
Rewrite the absolute value inequality as a compound inequality:

\[
-10 \leq 6 - 5x \leq 10
\]

### Step 2: Solve the Compound Inequality
Let's split the compound inequality and solve it:

1. **Left Side**:

   \[
   -10 \leq 6 - 5x
   \]

   Subtract 6 from both sides:

   \[
   -10 - 6 \leq -5x
   \]

   Simplify:

   \[
   -16 \leq -5x
   \]

   Divide by \(-5\) (flip the inequality sign):

   \[
   \frac{-16}{-5} \geq x
   \]

   Simplify:

   \[
   \frac{16}{5} \geq x \quad \text{or} \quad x \leq \frac{16}{5}
   \]

2. **Right Side**:

   \[
   6 - 5x \leq 10
   \]

   Subtract 6 from both sides:

   \[
   -5x \leq 4
   \]

   Divide by \(-5\) (flip the inequality sign):

   \[
   x \geq \frac{4}{-5}
   \]

   Simplify:

   \[
   x \geq -\frac{4}{5}
   \]

### Step 3: Combine the Results
Combine the two inequalities:

\[
-\frac{4}{5} \leq x \leq \frac{16}{5}
\]

### Step 4: Match the Solution to the Choices
The correct answer is:

**Option c: \(-\frac{4}{5} \leq x \leq \frac{16}{5}\)**

Would you like to see more details or have any other questions?

### Related Questions:
1. How do you solve compound inequalities involving absolute values?
2. What are the key steps when dealing with absolute value inequalities?
3. How does flipping the inequality sign affect the solution?
4. Can you explain why absolute values split into two inequalities?
5. How would this process change if the inequality were \(|6 - 5x| > 10\)?

### Tip:
Always check your final answer by substituting boundary values into the original inequality to ensure the solution set is correct!

Tentukan himpunan pertidaksamaan berikut: |6 - 5x| ≤ 10

Learn how to solve the absolute value inequality |6 - 5x| ≤ 10 using compound inequalities. This problem covers key algebraic concepts such as absolute values and solving inequalities. Suitable for Grades 9-10.

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