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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 1/x+1/[ln(1-x)] <1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
1 / x + 1 / ( ln ( 1 - x ) ) <1 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of ln
1 - x > 0 (3 )
From the definition field of divisor
ln ( 1 - x ) ≠ 0 (4 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < 1
From inequality(4):
x < 0 或 x > 0
From inequalities (1) and (2)
x < 0 或 x > 0 (5)
From inequalities (3) and (5)
x < 0 或 0 < x < 1 (6)
From inequalities (4) and (6)
x < 0 或 0 < x < 1 (7)
The final solution set is :
x < 0 或 0 < x < 1 Your problem has not been solved here? Please take a look at the hot problems !