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Assignment:Find the solution set of inequality 10000/x+10000/(x+8)*0+10000/(x+16)+10000/(x+24)*2 <= 150 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
10000 / x + 10000 / ( x + 8 ) * 0 + 10000 / ( x + 16 ) + 10000 / ( x + 24 ) * 2 <= 150 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of divisor
x + 8 ≠ 0 (3 )
From the definition field of divisor
x + 16 ≠ 0 (4 )
From the definition field of divisor
x + 24 ≠ 0 (5 )
From inequality(1):
x ≤ -24 或 -19.00498 ≤ x ≤ -16 或 -5.365795 ≤ x ≤ 0
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < -8 或 x > -8
From inequality(4):
x < -16 或 x > -16
From inequality(5):
x < -24 或 x > -24
From inequalities (1) and (2)
x ≤ -24 或 -19.00498 ≤ x ≤ -16 或 -5.365795 ≤ x < 0 (6)
From inequalities (3) and (6)
x ≤ -24 或 -19.00498 ≤ x ≤ -16 或 -5.365795 ≤ x < 0 (7)
From inequalities (4) and (7)
x ≤ -24 或 -19.00498 ≤ x < -16 或 -5.365795 ≤ x < 0 (8)
From inequalities (5) and (8)
x < -24 或 -19.00498 ≤ x < -16 或 -5.365795 ≤ x < 0 (9)
The final solution set is :
x < -24 或 -19.00498 ≤ x < -16 或 -5.365795 ≤ x < 0Your problem has not been solved here? Please take a look at the hot problems !