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Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]^2 + 2[x + 2] - 7 = 0 has : (1) exactly two solutions. (2) exactly four integral solutions. (3) infinitely many solutions. (4) no integral solution.

1. exactly two solutions.
2. exactly four integral solutions.
3. infinitely many solutions.
4. no integral solution.

Correct answer: exactly four integral solutions.

Solution

The equation involves the greatest integer function, which creates piecewise linear segments. By analyzing the intervals defined by integer values, we find that there are four distinct integer solutions that satisfy the equation.

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