To determine the total number of students that the science club can feed with \( x \) pizzas, we start with the following information:
- Each pizza contains 8 slices.
- Each student consumes 2 slices.
First, we find the total number of slices available from \( x \) pizzas: \[ \text{Total slices} = 8 \times x = 8x \]
Next, we find out how many students can be fed with the total number of slices. Since each student consumes 2 slices, we can calculate the number of students \( S \) that can be fed as follows: \[ S = \frac{\text{Total slices}}{\text{Slices per student}} = \frac{8x}{2} \]
Now, simplifying this expression: \[ S = 4x \]
Thus, the algebraic expression for the total number of students that the science club can feed pizza is: \[ \boxed{4x} \]