1. **Problem Statement:** We are given a parallelogram ABCD with diagonals AC and BD intersecting at point O. The diagonal BD is divided into segments BO and OD, where BO = $7x + 4$ and OD = 18. We need to find the value of $x$. 2. **Key Property:** In a parallelogram, the diagonals bisect each other. This means that point O is the midpoint of diagonal BD, so BO = OD. 3. **Set up the equation:** Since BO = OD, we have: $$7x + 4 = 18$$ 4. **Solve for $x$:** Subtract 4 from both sides: $$7x = 18 - 4$$ $$7x = 14$$ Divide both sides by 7: $$x = \frac{14}{7} = 2$$ 5. **Answer:** The value of $x$ is 2.