1. **State the problem:** We have a triangle with a segment dividing the base into two parts: one part is 3 units, the other is $x$ units. The left side of the triangle is 8 units, and the right side of the smaller triangle is 5 units. We need to find the value of $x$. 2. **Use the Angle Bisector Theorem:** This theorem states that the angle bisector divides the opposite side into segments proportional to the adjacent sides. So, $$\frac{x}{3} = \frac{8}{5}$$ 3. **Solve for $x$:** $$x = 3 \times \frac{8}{5}$$ 4. **Calculate:** $$x = \frac{3 \times 8}{5} = \frac{24}{5} = 4.8$$ 5. **Final answer:** $$x = 4.8$$ This means the segment $x$ is 4.8 units long.