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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality (-2+√(4+8x(x+3)))/(4x) >-1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
         ( -2 + √ ( 4 + 8 * x * ( x + 3 ) ) ) / ( 4 * x ) > -1         (1)
        From the definition field of √
         4 + 8 * x * ( x + 3 ) ≥ 0        (2 )
        From the definition field of divisor
         4 * x ≠ 0        (3 )

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    From inequality(1)：
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(2)：
         x ≤ -2.822876 或  x ≥ -0.177124
    From inequality(3)：
         x < 0 或  x ＞ 0

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    From inequalities (1) and (2)
         x ≤ -2.822876 或  x ≥ -0.177124    (4)
    From inequalities (3) and (4)
         x ≤ -2.822876 或  -0.177124 ≤ x < 0 或  x ＞ 0    (5)

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    The final solution set is :
         x ≤ -2.822876 或  -0.177124 ≤ x < 0 或  x ＞ 0

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