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Assignment:Find the solution set of inequality 250-[10000/x+20000/(x+60)] ≥17500/x+10000/(x+60) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
250 - ( 10000 / x + 20000 / ( x + 60 ) ) ≥17500 / x + 10000 / ( x + 60 ) (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of divisor
x + 60 ≠ 0 (3 )
17500 / x + 10000 / ( x + 60 ) >0 (4)
From the definition field of divisor
x ≠ 0 (5 )
From the definition field of divisor
x + 60 ≠ 0 (6 )
From inequality(1):
x ≤ -60 或 -32.57976 ≤ x ≤ 0
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < -60 或 x > -60
From inequality(4):
-60 < x < -420/11 或 x > 0
From inequality(5):
x < 0 或 x > 0
From inequality(6):
x < -60 或 x > -60
From inequalities (1) and (2)
x ≤ -60 或 -32.57976 ≤ x < 0 (7)
From inequalities (3) and (7)
x < -60 或 -32.57976 ≤ x < 0 (8)
From inequalities (4) and (8)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (9)
From inequalities (5) and (9)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (10)
From inequalities (6) and (10)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (11)
The final solution set is :
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!Your problem has not been solved here? Please take a look at the hot problems !