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How many integers satisfy the inequality

\left| \frac { 10(x+1) } {x^2 + 2x + 3 } \right| \geq 1?

  • math -

    10(x+1)/(x^2+2x+3) >= 1
    since x^2+2x+3 > 0,
    10x+10 >= x^2+2x+3
    x^2 - 8x - 7 <= 0

    So, all integers n such that

    4-√23 <= n <= 4+√23

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