https://file.aiquickdraw.com/mathbot/file/17263236827712am209ha.jpg

The inequality given in the image is:

\[
x - 3 \leq \frac{1}{3}x + 1
\]

### Step-by-step solution:

1. **Move all terms involving \(x\) to one side:**
   \[
   x - \frac{1}{3}x \leq 1 + 3
   \]

2. **Simplify:**
   \[
   \left(1 - \frac{1}{3}\right)x \leq 4
   \]
   \[
   \frac{2}{3}x \leq 4
   \]

3. **Solve for \(x\):**
   Multiply both sides by \(\frac{3}{2}\):
   \[
   x \leq 4 \times \frac{3}{2}
   \]
   \[
   x \leq 6
   \]

### Solution in set-builder notation:
The solution is \( x \leq 6 \). In set-builder notation, this is:
\[
\{x \mid x \leq 6\}
\]

The correct answer is option **D**.

---

Would you like further details or clarification? Here are some related questions:

1. How do you solve inequalities involving fractions?
2. What are the steps to convert an inequality into set-builder notation?
3. Can you explain how to interpret inequalities graphically?
4. What is the importance of isolating \(x\) in inequalities?
5. How does multiplying or dividing by a fraction affect inequalities?

**Tip:** When solving inequalities, always pay attention to whether you need to flip the inequality sign, especially when multiplying or dividing by negative numbers.

Use the x-intercept method to solve the inequality: x - 3 ≤ (1/3)x + 1. Write the solution in set-builder notation.

Learn how to solve the linear inequality x - 3 ≤ (1/3)x + 1 using the x-intercept method. This example covers fundamental algebraic principles of isolating variables and simplifying inequalities, suitable for students in Grades 8-10.

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