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Bot GPT-4o Given that \( AO = 2x + 5 \) and \( OD = 3x - 5 \), let's assume that \( AO \) and \( OD \) are parts of the same line segment or some geometric relationship where they are equal or part of the same length.
In most common cases when we have such algebraic expressions for segments, they usually add up to form a total length or are compared directly to each other. However, in this specific problem, it is not explicitly mentioned how \( AO \) and \( OD \) relate geometrically.
To move forward, we will assume the simplest case where \( AO \) and \( OD \) are equal (since no additional information is provided):
\[ AO = OD \]
So we set the expressions equal:
\[ 2x + 5 = 3x - 5 \]
To solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[ 5 = x - 5 \]
2. Add 5 to both sides:
\[ 10 = x \]
Thus, the solution is:
\[ x = 10 \]
So the correct answer is:
10