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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 2√(x+1)+√(2x-3)+√(15-3x) <2√19 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        2 * √ ( x + 1 ) + √ ( 2 * x - 3 ) + √ ( 15 - 3 * x ) <2 * √ 19         (1)
        From the definition field of √
         x + 1 ≥ 0        (2 )
        From the definition field of √
         2 * x - 3 ≥ 0        (3 )
        From the definition field of √
         15 - 3 * 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):
         x ≥ -1
    From inequality(3):
         x ≥ 3/2
    From inequality(4):
         x ≤ 5

    From inequalities (1) and (2)
         x ≥ -1    (5)
    From inequalities (3) and (5)
         x ≥ 3/2    (6)
    From inequalities (4) and (6)
         3/2 ≤ x ≤ 5    (7)

    The final solution set is :

         3/2 ≤ x ≤ 5




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