Let's analyze the problem in the image:

1. Leah is making a square picture frame and divides a piece of wood into 4 equal pieces.
2. Each side of the frame should be at most 12 inches.
3. Let $x$ represent the perimeter of the frame.

In a square, the perimeter $x$ is divided into 4 equal sides. Since each side must be less than or equal to 12 inches, the inequality that describes the problem is:

$\frac{x}{4} \leq 12$

Solving the inequality:

To solve for $x$, we can multiply both sides of the inequality by 4:

$\frac{x}{4} \times 4 \leq 12 \times 4$

$x \leq 48$

Thus, the perimeter of the picture frame will be at most 48 inches.

Do you have any questions or want more details on this? Here are 5 related questions:

1. What is the formula for the perimeter of a square?
2. How do you solve inequalities in general?
3. Can you give an example of a real-life application for inequality solutions?
4. What happens if Leah's frame sides are exactly 12 inches long?
5. How would the solution change if Leah wanted the perimeter to be strictly less than 48 inches?

Tip: When solving inequalities, remember to reverse the inequality sign if you multiply or divide both sides by a negative number!