Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality -2000+(500/(1+r))+(700/(1+r)^2)+(2000/(1+r)^2) >-10000+(8000/(1+r))+(2500/(1+r)^2)+(2000/(1+r)^2) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        -2000 + ( 500 / ( 1 + r ) ) + ( 700 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 ) > -10000 + ( 8000 / ( 1 + r ) ) + ( 2500 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 )         (1)
        From the definition field of divisor
         1 + x ≠ 0        (2 )
        From the definition field of divisor
         1 + x ≠ 0        (3 )
        From the definition field of divisor
         1 + x ≠ 0        (4 )
         -10000 + ( 8000 / ( 1 + r ) ) + ( 2500 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 ) >0         (5)
        From the definition field of divisor
         1 + x ≠ 0        (6 )
        From the definition field of divisor
         1 + x ≠ 0        (7 )
        From the definition field of divisor
         1 + x ≠ 0        (8 )

    From inequality(1):
         r < -1.198128 或  r > 0.135628
    From inequality(2):
         r < -1 或  r > -1
    From inequality(3):
         r < -1 或  r > -1
    From inequality(4):
         r < -1 或  r > -1
    From inequality(5):
         -1.381025 < r < 0.181025
    From inequality(6):
         r < -1 或  r > -1
    From inequality(7):
         r < -1 或  r > -1
    From inequality(8):
         r < -1 或  r > -1

    From inequalities (1) and (2)
         r < -1.198128 或  r > 0.135628    (9)
    From inequalities (3) and (9)
         r < -1.198128 或  r > 0.135628    (10)
    From inequalities (4) and (10)
         r < -1.198128 或  r > 0.135628    (11)
    From inequalities (5) and (11)
         -1.381025 < r < -1.198128 或  0.135628 < r < 0.181025     (12)
    From inequalities (6) and (12)
         -1.381025 < r < -1.198128 或  0.135628 < r < 0.181025     (13)
    From inequalities (7) and (13)
         -1.381025 < r < -1.198128 或  0.135628 < r < 0.181025     (14)
    From inequalities (8) and (14)
         -1.381025 < r < -1.198128 或  0.135628 < r < 0.181025     (15)

    The final solution set is :

         -1.381025 < r < -1.198128 或  0.135628 < r < 0.181025




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