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Hello everyone! Today we are looking at a problem involving a symbolic operation. We need to compare variables A and B based on the definition provided in the question.
To evaluate the operation, we use the definition for the known values of A. Substituting these into the equation, we get A equals four times the quantity b plus two, minus three times two, plus negative one.
Now for the simplification of equation A. Starting from our substituted formula, we get A equals four b plus eight minus six minus one, which simplifies to A equals four b plus one.
Comparing A and B, we have B equals four. Since b is a natural number from the set one, two, three, and so on, testing the smallest value b equals one gives A equals four times one plus one, which equals five.
In conclusion, since A is at least five and B is four, A is greater than B. Thus, option A, A is greater than B, is the correct answer.