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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality sqrtx <0.5x     Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities：
         sqrt x <0.5 * x         (1)
        From the definition field of √
        x ≥ 0        (2 )
        0.5 * x < sqrt ( sqrt ( 2 * x ) )         (3)
        From the definition field of √
         2 * x ≥ 0        (4 )
        From the definition field of √
         sqrt ( 2 * x ) ≥ 0        (5 )

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    From inequality(1)：
         x < 0 或  x ＞ 4
    From inequality(2)：
         x ≥ 0
    From inequality(3)：
         0 < x < 3.174802
    From inequality(4)：
         x ≥ 0
    From inequality(5)：
         x ≥ 0

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    From inequalities (1) and (2)
         x ＞ 4    (6)
    From inequalities (3) and (6)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (7)
    From inequalities (4) and (7)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (8)
    From inequalities (5) and (8)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (9)

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    The final solution set is :
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!

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