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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 ≤ 5Your problem has not been solved here? Please take a look at the hot problems !