https://file.aiquickdraw.com/mathbot/file/17272702364598wrf32su.jpg

The problem in the image asks to find the area of a rectangle, where the dimensions are given as \( x + 6 \) and \( x + 1 \). 

### Step-by-Step Solution:

The formula for the area \( A \) of a rectangle is:

\[
A = \text{length} \times \text{width}
\]

Here, the length is \( x + 6 \) and the width is \( x + 1 \).

So, the area \( A \) can be written as:

\[
A = (x + 6)(x + 1)
\]

Now, expand this expression using the distributive property (also known as the FOIL method):

\[
A = (x + 6)(x + 1) = x(x + 1) + 6(x + 1)
\]

Expanding each term:

\[
A = x^2 + x + 6x + 6
\]

Combine like terms:

\[
A = x^2 + 7x + 6
\]

Thus, the area of the rectangle is:

\[
A = x^2 + 7x + 6
\]

This is the simplified expression for the area.

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Would you like further clarification on any step?

Here are 5 related questions for practice:
1. What is the area of the rectangle if \( x = 3 \)?
2. How would the area change if the dimensions were \( x + 5 \) and \( x + 2 \)?
3. What are the steps for factoring the area expression \( x^2 + 7x + 6 \)?
4. How can you graph the equation \( A = x^2 + 7x + 6 \) to visualize the area?
5. If the perimeter of the rectangle is required, how would you calculate it?

**Tip:** Always double-check your algebraic expansions and combine like terms carefully to avoid mistakes.

Find the area. Simplify your answer. Given dimensions are (x + 6) and (x + 1).

Learn how to find the area of a rectangle with dimensions (x + 6) and (x + 1) by expanding the polynomial and simplifying the expression. This algebra problem is suitable for students in Grades 7-9.

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