https://file.aiquickdraw.com/mathbot/file/1726708588226he87o5xf.jpg

The problem asks for a simplified expression for the area of a rectangle. Based on the image, the dimensions of the rectangle are given as:

- Length: \(12x - 6\) inches
- Width: \(4 \frac{1}{6}\) inches, which can be converted to an improper fraction as \( \frac{25}{6} \) inches.

To find the area of a rectangle, we use the formula:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

### Step 1: Multiply the expressions
The length is \(12x - 6\), and the width is \( \frac{25}{6} \). So, the area becomes:

\[
\text{Area} = (12x - 6) \times \frac{25}{6}
\]

### Step 2: Distribute the fraction
Distribute \( \frac{25}{6} \) to both terms inside the parentheses:

\[
\text{Area} = \frac{25}{6} \times 12x - \frac{25}{6} \times 6
\]

### Step 3: Simplify
First, simplify each multiplication:

\[
\frac{25}{6} \times 12x = \frac{25 \times 12x}{6} = 50x
\]
\[
\frac{25}{6} \times 6 = \frac{25 \times 6}{6} = 25
\]

Thus, the expression for the area becomes:

\[
\text{Area} = 50x - 25 \, \text{square inches}
\]

This is the simplified expression for the area of the rectangle.

---

Would you like further details or have any other questions? 

Here are 5 related questions to explore:
1. How would the area change if the width of the rectangle doubled?
2. Can the expression for the length \(12x - 6\) be factored further?
3. How would the calculation change if the width was in a different unit, like centimeters?
4. What happens to the area expression if \(x = 0\)?
5. How does the area vary as \(x\) increases?

**Tip**: When working with mixed fractions, it's often helpful to convert them to improper fractions before multiplying!

Write a simplified expression for the area of the rectangle with dimensions 12x - 6 inches and 4 1/6 inches.

Learn how to simplify the area expression for a rectangle with dimensions 12x - 6 inches and 4 1/6 inches. This problem involves algebraic multiplication and conversion of mixed numbers to improper fractions. Suitable for students in Grades 7-9.

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