Algebra Level 4

A teacher has given the following equation to his four best students, and then asked how many integer answers it had.

[12x+1x+12]=10 \left [ \dfrac{12x+1}{x+12} \right ] = 10

Al considered his teacher's notation to be a mere parenthesis, and quickly shouted his answer. Bob considered [x] \left [ x \right ] the floor function, and answered in time with his fellows Carl (which used the round function for his solution) and Dan (which preferred the ceiling function).

Which boy gave out the biggest answer?


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