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Verified Answer :

A\(\frac{x - 6}{2} = x + 13\) has one solution.

B) \(2 + 6x - 7 = 8 + 2x - 10 + 4x\) has no solution.

C) \(3x + 5 = \frac{1}{5} (15x + 10)\) has no solution.

D) \(\frac{1}{4} (16 + 8x) = 3x - 1 - x + 5\) has infinite solutions.

Answer: \(\fbox {1. A} \\ \fbox {2. B} \\ \fbox {3. B} \\ \fbox {4. C}\)