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Baltic Way competition problems, 1992

Algebra Difficulty 4.5 AIME Prove it Baltic Way

Problem:
Find all integers satisfying the equation $2^{x} \cdot (4 - x) = 2x + 4$ .

Solution

Solution:
Since $2^{x}$ must be positive, we have $\frac{2x + 4}{4 - x} > 0$ yielding $-2 < x < 4$ . Thus it suffices to check the points $-1, 0, 1, 2, 3$ . The three solutions are $x = 0, 1, 2$ .

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