https://file.aiquickdraw.com/mathbot/file/1729883860538g4xqxef7.jpg

Let's analyze the given problem.

### Step 1: Cost Comparison of Painting for Studio A and Studio B
- **Art Studio A** charges **$13.00 per hour**, and the canvas is included.
- **Art Studio B** charges **$10.75 per hour**, and the canvas costs an additional **$12.00**.

We need to find when **Studio B's total cost** is **less than Studio A's total cost** for **painting**.

### Step 2: Form the Cost Expressions
Let $ x $ represent the number of hours.

- **Studio A's total cost for $ x $ hours**: 
  \[
  C_A = 13x
  \]
- **Studio B's total cost for $ x $ hours**: 
  \[
  C_B = 10.75x + 12
  \]

### Step 3: Set Up the Inequality
We are asked to find when **Studio B is less expensive** than Studio A:
\[
C_B < C_A
\]
Substitute the cost expressions:
\[
10.75x + 12 < 13x
\]

### Step 4: Solve the Inequality
Now, solve for $ x $:
\[
10.75x + 12 < 13x
\]
Subtract $ 10.75x $ from both sides:
\[
12 < 13x - 10.75x
\]
\[
12 < 2.25x
\]
Divide both sides by 2.25:
\[
x > \frac{12}{2.25}
\]
\[
x > 5.33 \quad \text{or} \quad x > 5 \frac{1}{3}
\]

### Step 5: Conclusion
The inequality that represents the number of hours when Studio B costs less than Studio A is:
\[
x > 5 \frac{1}{3}
\]
So, the correct answer is **Option D**.

Would you like any further details or explanations? Here are some related questions to explore further:

1. What would the cost difference be if you worked for exactly 5 hours?
2. How do the pricing structures for the vase and clay pottery differ between the studios?
3. Can we represent the cost difference graphically for various hours?
4. If the supply cost for vases increased, how would that affect the inequality for vases?
5. How would this inequality change if Studio B gave a discount on canvas?

**Tip**: When comparing costs, always set up inequalities and solve them step by step, keeping track of all variables and constants.

Which inequality represents the number of hours, x, when art studio B costs less for painting than art studio A?

Learn how to solve an inequality comparing the costs of two art studios for painting projects. This problem involves basic algebra, including setting up and solving linear inequalities. Suitable for Grades 8-10 students looking to understand cost comparisons using math.

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