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☆1 inequalities
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Assignment:Find the solution set of inequality -2000+500/(1+x)+700/((1+x)^2)+(2000/(1+x)^3) <-10000+8000/(1+x)+2500/((1+x)^2)+(2000/(1+x)^3) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
-2000 + 500 / ( 1 + x ) + 700 / ( ( 1 + x ) ^ 2 ) + ( 2000 / ( 1 + x ) ^ 3 ) < -10000 + 8000 / ( 1 + x ) + 2500 / ( ( 1 + x ) ^ 2 ) + ( 2000 / ( 1 + x ) ^ 3 ) (1)
From the definition field of divisor
1 + x ≠ 0 (2 )
From the definition field of divisor
( 1 + x ) ^ 2 ≠ 0 (3 )
From the definition field of divisor
1 + x ≠ 0 (4 )
From the definition field of divisor
1 + x ≠ 0 (5 )
From the definition field of divisor
( 1 + x ) ^ 2 ≠ 0 (6 )
From the definition field of divisor
1 + x ≠ 0 (7 )
From inequality(1):
-1.198128 < x < 0.135628
From inequality(2):
x < -1 或 x > -1
From inequality(3):
x < -1 或 x > -1
From inequality(4):
x < -1 或 x > -1
From inequality(5):
x < -1 或 x > -1
From inequality(6):
x < -1 或 x > -1
From inequality(7):
x < -1 或 x > -1
From inequalities (1) and (2)
-1.198128 < x < -1 或 -1 < x < 0.135628 (8)
From inequalities (3) and (8)
-1.198128 < x < -1 或 -1 < x < -1 或 -1 < x < 0.135628 (9)
From inequalities (4) and (9)
-1.198128 < x < -1 或 -1 < x < -1 或 -1 < x < 0.135628 (10)
From inequalities (5) and (10)
-1.198128 < x < -1 或 -1 < x < -1 或 -1 < x < 0.135628 (11)
From inequalities (6) and (11)
-1.198128 < x < -1 或 -1 < x < -1 或 或 -1 < x < 0.135628 (12)
From inequalities (7) and (12)
-1.198128 < x < -1 或 -1 < x < -1 或 或 -1 < x < 0.135628 (13)
The final solution set is :
-1.198128 < x < -1 或 -1 < x < -1 或 或 -1 < x < 0.135628 Your problem has not been solved here? Please take a look at the hot problems !