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