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Algebra Level 4

loga(x2x+2)>loga(x2+2x+3) \log_a(x^2 - x + 2) > \log_a(-x^2 + 2x + 3)

If x=49 x = \frac{4}{9} satisfies the above inequality, then find the sum of all integer solutions of xx to the inequality.


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