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Assignment:Find the solution set of inequality [2/(x-0.2)]+[2/(x-0.04)]+[2/(x-0.12)] ≤[x/(0.1x-0.02)] .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 2 / ( x - 0.2 ) ) + ( 2 / ( x - 0.04 ) ) + ( 2 / ( x - 0.12 ) ) ≤ ( x / ( 0.1 * x - 0.02 ) ) (1)
From the definition field of divisor
x - 0.2 ≠ 0 (2 )
From the definition field of divisor
x - 0.04 ≠ 0 (3 )
From the definition field of divisor
x - 0.12 ≠ 0 (4 )
From the definition field of divisor
0.1 * x - 0.02 ≠ 0 (5 )
From inequality(1):
x ≤ 0.12 或 x ≥ 0.483961
From inequality(2):
x < 1/5 或 x > 1/5
From inequality(3):
x < 1/25 或 x > 1/25
From inequality(4):
x < 3/25 或 x > 3/25
From inequality(5):
x < 1/5 或 x > 1/5
From inequalities (1) and (2)
x ≤ 0.12 或 x ≥ 0.483961 (6)
From inequalities (3) and (6)
x < 1/25 或 1/25 < x ≤ 0.12 或 x ≥ 0.483961 (7)
From inequalities (4) and (7)
x < 1/25 或 1/25 < x < 3/25 或 x ≥ 0.483961 (8)
From inequalities (5) and (8)
x < 1/25 或 1/25 < x < 3/25 或 x ≥ 0.483961 (9)
The final solution set is :
x < 1/25 或 1/25 < x < 3/25 或 x ≥ 0.483961Your problem has not been solved here? Please take a look at the hot problems !