1. **State the problem:** We need to find the value of the function $g(x) = \frac{7}{8}x - \frac{1}{2}$ at $x=7$. 2. **Formula used:** To find $g(7)$, substitute $x=7$ into the function: $$g(7) = \frac{7}{8} \times 7 - \frac{1}{2}$$ 3. **Calculate the multiplication:** $$\frac{7}{8} \times 7 = \frac{7 \times 7}{8} = \frac{49}{8}$$ 4. **Subtract $\frac{1}{2}$ from $\frac{49}{8}$:** First, express $\frac{1}{2}$ with denominator 8: $$\frac{1}{2} = \frac{4}{8}$$ Now subtract: $$\frac{49}{8} - \frac{4}{8} = \frac{45}{8}$$ 5. **Final answer:** $$g(7) = \frac{45}{8}$$ This corresponds to option B. **Explanation:** We evaluated the function by substituting the given $x$ value, carefully performed multiplication and subtraction of fractions by finding a common denominator, and simplified to get the final result.