In a rectangle, the diagonals bisect each other. This means that segments AO and BO must be equal in length at point O. So, we set up the equation based on the given segments:
\[ AO = BO \]
Substituting the expressions for AO and BO, we get:
\[ 4x - 3 = 5x - 10 \]
Now, we can solve for \( x \):
- Subtract \( 4x \) from both sides:
\[ -3 = x - 10 \]
- Add 10 to both sides:
\[ 7 = x \]
Thus, the value of \( x \) is \( 7 \).
The correct answer is x = 7.
This solution works because it is based on the property of rectangles that states the diagonals bisect each other, leading to the equality of the segments.