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 10 >1.5*0.5/1.4*x*(1/(1-e^(-0.1*x))*e^(-0.1*x)-1/(1-e^(-1.5*x))*e^(-1.5*x)) >3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        10 >1.5 * 0.5 / 1.4 * x * ( 1 / ( 1 - e ^ ( -0.1 * x ) ) * e ^ ( -0.1 * x ) - 1 / ( 1 - e ^ ( -1.5 * x ) ) * e ^ ( -1.5 * x ) )         (1)
        1.5 * 0.5 / 1.4 * x * ( 1 / ( 1 - e ^ ( -0.1 * x ) ) * e ^ ( -0.1 * x ) - 1 / ( 1 - e ^ ( -1.5 * x ) ) * e ^ ( -1.5 * x ) ) >3         (2)
        From the definition field of divisor
         1 - e ^ ( -0.1 * x ) ≠ 0        (3 )
        From the definition field of divisor
         1 - e ^ ( -1.5 * x ) ≠ 0        (4 )

    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):
         -√397610951/√3500000 < x < √397610951/√3500000
    From inequality(3):
         x < 0 或  x > 0
    From inequality(4):
         x < 0 或  x > 0

    From inequalities (1) and (2)
         -√397610951/√3500000 < x < √397610951/√3500000     (5)
    From inequalities (3) and (5)
         -√397610951/√3500000 < x < 0 或  0 < x < √397610951/√3500000     (6)
    From inequalities (4) and (6)
         -√397610951/√3500000 < x < 0 或  0 < x < √397610951/√3500000     (7)

    The final solution set is :

         -√397610951/√3500000 < x < 0 或  0 < x < √397610951/√3500000




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