To determine the correct inequality that represents the situation described:
1. Define Variables:
- Let [tex]\( x \)[/tex] represent the width of the photo (in inches).
2. Width of Cake:
- The width of the cake is 4 inches more than the width of the photo. Therefore, the width of the cake is [tex]\( x + 4 \)[/tex].
3. Length of Cake:
- The length of the cake is two times its width. Thus, the length of the cake is [tex]\( 2(x + 4) \)[/tex].
4. Calculate Area of Cake:
- The area of a rectangle is given by the formula: Area = Length × Width.
- Substituting the expressions for the length and width of the cake, we get:
[tex]\[
\text{Area}_\text{cake} = (x + 4) \times 2(x + 4)
\][/tex]
5. Simplify the Expression:
- First, expand the expression:
[tex]\[
\text{Area}_\text{cake} = (x + 4)(2x + 8)
\][/tex]
6. Set Up the Inequality:
- We are given that the area of the cake is at least 254 square inches. Therefore, we set up the inequality:
[tex]\[
(x + 4)(2x + 8) \geq 254
\][/tex]
The inequality [tex]\( (x + 4)(2x + 8) \geq 254 \)[/tex] matches option C.
Thus, the correct answer is:
C. [tex]\( 2x^2 + 16x + 32 \geq 254 \)[/tex]
