Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 2 questions will be solved this time.Among them
           ☆2 inequalities

[ 1/2Inequality]
    Assignment:Find the solution set of inequality 0 <10000/x+20000/(x+60) ≤10000/7, .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        0 <10000 / x + 20000 / ( x + 60 )         (1)
        10000 / x + 20000 / ( x + 60 ) ≤10000 / 7 ,         (2)
        From the definition field of divisor
        x ≠ 0        (3 )
        From the definition field of divisor
         x + 60 ≠ 0        (4 )

    From inequality(1):
         -60 < x < -20 或  x > 0
    From inequality(2):
         x ≤ -60 或  -47.78869 ≤ x ≤ 0 或  x ≥ 8.78869
    From inequality(3):
         x < 0 或  x > 0
    From inequality(4):
         x < -60 或  x > -60

    From inequalities (1) and (2)
         -47.78869 ≤ x < -20 或  x ≥ 8.78869    (5)
    From inequalities (3) and (5)
         -47.78869 ≤ x < -20 或  x ≥ 8.78869    (6)
    From inequalities (4) and (6)
         -47.78869 ≤ x < -20 或  x ≥ 8.78869    (7)

    The final solution set is :

         -47.78869 ≤ x < -20 或  x ≥ 8.78869

[ 2/2Inequality]
    Assignment:Find the solution set of inequality 250-[10000/x+20000/(x+60)] ≥17500/x+20000/(x+60) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        250 - ( 10000 / x + 20000 / ( x + 60 ) ) ≥17500 / x + 20000 / ( x + 60 )         (1)
        From the definition field of divisor
        x ≠ 0        (2 )
        From the definition field of divisor
         x + 60 ≠ 0        (3 )
        17500 / x + 20000 / ( x + 60 ) >0         (4)
        From the definition field of divisor
        x ≠ 0        (5 )
        From the definition field of divisor
         x + 60 ≠ 0        (6 )

    From inequality(1):
         x ≤ -60 或  -27.75918 ≤ x ≤ 0
    From inequality(2):
         x < 0 或  x > 0
    From inequality(3):
         x < -60 或  x > -60
    From inequality(4):
         -60 < x < -28 或  x > 0
    From inequality(5):
         x < 0 或  x > 0
    From inequality(6):
         x < -60 或  x > -60

    From inequalities (1) and (2)
         x ≤ -60 或  -27.75918 ≤ x < 0    (7)
    From inequalities (3) and (7)
         x < -60 或  -27.75918 ≤ x < 0    (8)
    From inequalities (4) and (8)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (9)
    From inequalities (5) and (9)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (10)
    From inequalities (6) and (10)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (11)

    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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