1. **State the problem:** We are given that segment BD bisects segment AC, meaning BD divides AC into two equal parts at point D. 2. **Identify given lengths:** AB = 8, BC = 7, DC = 4, and AD = x. 3. **Understand the bisector property:** Since BD bisects AC, point D is the midpoint of AC, so AD = DC. 4. **Set up the equation:** Because D is midpoint, we have $$x = 4$$ 5. **Conclusion:** The value of $x$ is 4. No rounding is necessary as $x$ is already a whole number.