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Assignment:Find the solution set of inequality -1200-800/(1+x)+600/(1+x)^2+370*[(1+x)^4-1]/[x*(1+x)^6]+550/(1+x)^7 >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
-1200 - 800 / ( 1 + x ) + 600 / ( 1 + x ) ^ 2 + 370 * ( ( 1 + x ) ^ 4 - 1 ) / ( x * ( 1 + x ) ^ 6 ) + 550 / ( 1 + x ) ^ 7 >0 (1)
From the definition field of divisor
1 + x ≠ 0 (2 )
From the definition field of divisor
1 + x ≠ 0 (3 )
From the definition field of divisor
x * ( 1 + x ) ^ 6 ≠ 0 (4 )
From the definition field of divisor
1 + x ≠ 0 (5 )
From inequality(1):
-1.019307 < x < 0.071938
From inequality(2):
x < -1 或 x > -1
From inequality(3):
x < -1 或 x > -1
From inequality(4):
x < -1 或 -1 < x < 0 或 x > 0
From inequality(5):
x < -1 或 x > -1
From inequalities (1) and (2)
-1.019307 < x < -1 或 -1 < x < 0.071938 (6)
From inequalities (3) and (6)
-1.019307 < x < -1 或 -1 < x < 0.071938 (7)
From inequalities (4) and (7)
-1.019307 < x < -1 或 -1 < x < -1 或 -1 < x < 0 或 0 < x < 0.071938 (8)
From inequalities (5) and (8)
-1.019307 < x < -1 或 -1 < x < -1 或 -1 < x < 0 或 0 < x < 0.071938 (9)
The final solution set is :
-1.019307 < x < -1 或 -1 < x < -1 或 -1 < x < 0 或 0 < x < 0.071938 Your problem has not been solved here? Please take a look at the hot problems !