1. **State the problem:** Ezra runs some distance $d$ miles, then has $\frac{1}{2}$ mile left to run, and the total distance he planned to run is $\frac{3}{4}$ mile. We want to find $d$. 2. **Write the equation:** The total distance is the distance run plus the distance left, so: $$d + \frac{1}{2} = \frac{3}{4}$$ 3. **Solve for $d$:** Subtract $\frac{1}{2}$ from both sides: $$d + \cancel{\frac{1}{2}} - \cancel{\frac{1}{2}} = \frac{3}{4} - \frac{1}{2}$$ 4. **Calculate the right side:** Convert $\frac{1}{2}$ to $\frac{2}{4}$ to subtract easily: $$d = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$$ 5. **Interpretation:** Ezra ran $\frac{1}{4}$ mile before twisting his ankle. **Final answer:** $$d = \frac{1}{4}$$