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Assignment:Find the solution set of inequality 269 >x
x >89 .
Question type: Inequality
Solution:
The inequality can be reduced to 4 inequalities:
269 > x (1)
x < tan x (2)
tan x > x (3)
x >89 (4)
From inequality(1):
x < 269
From inequality(2):
x < -7.853982 或 -7.725252 < x < -4.712389 或 -4.493409 < x < -1.570796 或 0 < x < 1.570796 或 4.493409 < x < 4.712389 或 x > 7.725252
From inequality(3):
x < -7.853982 或 -7.725252 < x < -4.712389 或 -4.493409 < x < -1.570796 或 0 < x < 1.570796 或 4.493409 < x < 4.712389 或 x > 7.725252
From inequality(4):
x > 89
From inequalities (1) and (2)
x < -7.853982 或 -7.725252 < x < -4.712389 或 -4.493409 < x < -1.570796 或 0 < x < 1.570796 或 4.493409 < x < 4.712389 或 7.725252 < x < 269 (5)
From inequalities (3) and (5)
x < -7.853982 或 -7.725252 < x < -4.712389 或 -4.493409 < x < -1.570796 或 0 < x < 1.570796 或 4.493409 < x < 4.712389 或 7.725252 < x < 269 (6)
From inequalities (4) and (6)
89 < x < 269 (7)
The final solution set is :
89 < x < 269
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