https://file.aiquickdraw.com/mathbot/file/17271089612927qnoggbs.jpg

The problem in the image reads:  
"The area of the rectangle is greater than 60 square feet. Find the possible values of *x*."

### Problem Breakdown:

The rectangle's dimensions are shown in the image as:
- One side is \( 12 \, \text{ft} \).
- The other side is \( x + 3 \, \text{ft} \).

The area \( A \) of a rectangle is given by:
\[
A = \text{length} \times \text{width}
\]
Here:
\[
A = 12 \times (x + 3)
\]

We are told that the area is greater than 60 square feet, so we can set up the inequality:
\[
12 \times (x + 3) > 60
\]

### Step-by-Step Solution:

1. Expand the left side:
\[
12(x + 3) = 12x + 36
\]
Thus, the inequality becomes:
\[
12x + 36 > 60
\]

2. Subtract 36 from both sides:
\[
12x > 24
\]

3. Divide both sides by 12:
\[
x > 2
\]

### Conclusion:
The possible values for \( x \) are all numbers greater than 2, i.e., \( x > 2 \).

---

Would you like more details on any part of the solution?  
Here are five related questions for further exploration:

1. What is the area of the rectangle when \( x = 5 \)?
2. How would the inequality change if the area was less than 60 square feet?
3. Can you generalize this method to find values of \( x \) for other rectangle dimensions?
4. What if one of the rectangle's dimensions was a quadratic function of \( x \)?
5. How does the solution change if the length or width of the rectangle varies with another variable?

**Tip:** When solving inequalities involving multiplication or division, remember to flip the inequality sign if you multiply or divide by a negative number!

The area of the rectangle is greater than 60 square feet. Find the possible values of x.

Learn how to solve an algebraic inequality involving the area of a rectangle where the area is greater than 60 square feet. This problem covers key concepts in algebra and geometry, including inequalities and the area of a rectangle. Suitable for students in Grades 6-8.

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