To determine the correct inequality, let's break down the problem mathematically step-by-step.
1. Define the variables:
- Let [tex]\(x\)[/tex] represent the width of the photo in the center of the cake (in inches).
2. Express the dimensions of the cake:
- The width of the cake is [tex]\(x + 4\)[/tex] inches (since the width is 4 inches more than the width of the photo).
- The length of the cake is double the width of the cake. Hence, the length is [tex]\(2 \times (x + 4) = 2x + 8\)[/tex] inches.
3. Calculate the area of the cake:
- The area of a rectangle is given by the product of its width and length.
- So, the area [tex]\(A\)[/tex] of the cake is [tex]\((x + 4) \cdot (2x + 8)\)[/tex].
4. Set up the inequality:
- Given that the area of the cake is at least 254 square inches, this can be translated into an inequality:
[tex]\[
(x + 4)(2x + 8) \geq 254
\][/tex]
We can see that this matches the answer in the question. Therefore, the correct inequality that represents this situation is:
[tex]\[
D. \ (x + 4)(2x + 8) \geq 254
\][/tex]
