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Assignment:Find the solution set of inequality sqrt(4*x-2)+2*sqrt(3-x) >2024/2023 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( 4 * x - 2 ) + 2 * sqrt ( 3 - x ) >2024 / 2023 (1)
From the definition field of √
4 * x - 2 ≥ 0 (2 )
From the definition field of √
3 - x ≥ 0 (3 )
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 ≥ 1/2
From inequality(3):
x ≤ 3
From inequalities (1) and (2)
x ≥ 1/2 (4)
From inequalities (3) and (4)
1/2 ≤ x ≤ 3 (5)
The final solution set is :
1/2 ≤ x ≤ 3Your problem has not been solved here? Please take a look at the hot problems !