Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 4/(4.2+X)*ln(1/(4.2+X))+(0.2)/(4.2+X)*ln(0.2/(4.2+X))+X/(4.2+X)*ln(X/(4.2+X))-1.5 <0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
        4 / ( 4.2 + X ) * ln ( 1 / ( 4.2 + X ) ) + ( 0.2 ) / ( 4.2 + X ) * ln ( 0.2 / ( 4.2 + X ) ) + X / ( 4.2 + X ) * ln ( X / ( 4.2 + X ) ) - 1.5 <0         (1)
        From the definition field of divisor
         4.2 + x ≠ 0        (2 )
        From the definition field of divisor
         4.2 + x ≠ 0        (3 )
        From the definition field of ln
         1 / ( 4.2 + x ) > 0        (4 )
        From the definition field of divisor
         4.2 + x ≠ 0        (5 )
        From the definition field of divisor
         4.2 + x ≠ 0        (6 )
        From the definition field of ln
         0.2 / ( 4.2 + x ) > 0        (7 )
        From the definition field of divisor
         4.2 + x ≠ 0        (8 )
        From the definition field of divisor
         4.2 + x ≠ 0        (9 )
        From the definition field of ln
         x / ( 4.2 + x ) > 0        (10 )

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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 < -21/5 或  X ＞ -21/5
    From inequality(3)：
         X < -21/5 或  X ＞ -21/5
    From inequality(4)：
         X ＞ -4.2
    From inequality(5)：
         X < -21/5 或  X ＞ -21/5
    From inequality(6)：
         X < -21/5 或  X ＞ -21/5
    From inequality(7)：
         X ＞ -4.2
    From inequality(8)：
         X < -21/5 或  X ＞ -21/5
    From inequality(9)：
         X < -21/5 或  X ＞ -21/5
    From inequality(10)：
         X < -4.2 或  X ＞ 0

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    From inequalities (1) and (2)
         X < -21/5 或  X ＞ -21/5    (11)
    From inequalities (3) and (11)
         X < -21/5 或  X ＞ -21/5    (12)
    From inequalities (4) and (12)
         X ＞ -4.2    (13)
    From inequalities (5) and (13)
         X ＞ -21/5    (14)
    From inequalities (6) and (14)
         X ＞ -21/5    (15)
    From inequalities (7) and (15)
         X ＞ -4.2    (16)
    From inequalities (8) and (16)
         X ＞ -21/5    (17)
    From inequalities (9) and (17)
         X ＞ -21/5    (18)
    From inequalities (10) and (18)
         X ＞ 0    (19)

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    The final solution set is :
         X ＞ 0

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