Mathematics
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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 4 questions will be solved this time.Among them
           ☆4 inequalities

[ 1/4Inequality]
    Assignment:Find the solution set of inequality (58x1+58x2+65.25x3+45.75x4)/(x1+x2+x3+x4) >= 58 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 58 * x * 1 + 58 * x * 2 + 65.25 * x * 3 + 45.75 * x * 4 ) / ( x * 1 + x * 2 + x * 3 + x * 4 ) >= 58         (1)
        From the definition field of divisor
         x * 1 + x * 2 + x * 3 + x * 4 ≠ 0        (2 )

    From inequality(1):
        The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
    From inequality(2):
         x < 0 或  x > 0

    The final solution set is :

        The solution set is empty,that is, the inequality will never be estatlished within the real number range.

[ 2/4Inequality]
    Assignment:Find the solution set of inequality (1.2x1+0.2x2+0.25x3+0.75x4)/(x1+x2+x3+x4) <= 1.3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 1.2 * x * 1 + 0.2 * x * 2 + 0.25 * x * 3 + 0.75 * x * 4 ) / ( x * 1 + x * 2 + x * 3 + x * 4 ) <= 1.3         (1)
        From the definition field of divisor
         x * 1 + x * 2 + x * 3 + x * 4 ≠ 0        (2 )

    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 < 0 或  x > 0

    From inequalities (1) and (2)
         x < 0 或  x > 0    (3)

    The final solution set is :

         x < 0 或  x > 0

[ 3/4Inequality]
    Assignment:Find the solution set of inequality (0.03x1+0.1x2+0.003x3+0.1x4)/(x1+x2+x3+x4) <= 0.1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 0.03 * x * 1 + 0.1 * x * 2 + 0.003 * x * 3 + 0.1 * x * 4 ) / ( x * 1 + x * 2 + x * 3 + x * 4 ) <= 0.1         (1)
        From the definition field of divisor
         x * 1 + x * 2 + x * 3 + x * 4 ≠ 0        (2 )

    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 < 0 或  x > 0

    From inequalities (1) and (2)
         x < 0 或  x > 0    (3)

    The final solution set is :

         x < 0 或  x > 0

[ 4/4Inequality]
    Assignment:Find the solution set of inequality (0.2x1+0.2x2+0.25x3+0.75x4)/(x1+x2+x3+x4) <= 1.2 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( 0.2 * x * 1 + 0.2 * x * 2 + 0.25 * x * 3 + 0.75 * x * 4 ) / ( x * 1 + x * 2 + x * 3 + x * 4 ) <= 1.2         (1)
        From the definition field of divisor
         x * 1 + x * 2 + x * 3 + x * 4 ≠ 0        (2 )

    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 < 0 或  x > 0

    From inequalities (1) and (2)
         x < 0 或  x > 0    (3)

    The final solution set is :

         x < 0 或  x > 0




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