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☆1 inequalities
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Assignment:Find the solution set of inequality lg(abs((-absx+4)abs(-absx+1))-1) ≤0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
lg ( abs ( ( -abs x + 4 ) * abs ( -abs x + 1 ) ) - 1 ) ≤0 (1)
From the definition field of lg
abs ( ( -abs x + 4 ) * abs ( -abs x + 1 ) ) - 1 > 0 (2 )
From inequality(1):
-4.561553 ≤ x ≤ -3 或 -2 ≤ x ≤ -0.438447 或 0.438447 ≤ x ≤ 2 或 3 ≤ x ≤ 4.561553
From inequality(2):
x < -4.302776 或 -3.618034 < x < -1.381966 或 -0.697224 < x < 0.697224 或 1.381966 < x < 3.618034 或 x > 4.302776
From inequalities (1) and (2)
-4.561553 ≤ x < -4.302776 或 -3.618034 < x ≤ -3 或 -2 ≤ x < -1.381966 或 -0.697224 < x ≤ -0.438447 或 0.438447 ≤ x < 0.697224 或 1.381966 < x ≤ 2 或 3 ≤ x < 3.618034 或 4.302776 < x ≤ 4.561553 (3)
The final solution set is :
-4.561553 ≤ x < -4.302776 或 -3.618034 < x ≤ -3 或 -2 ≤ x < -1.381966 或 -0.697224 < x ≤ -0.438447 或 0.438447 ≤ x < 0.697224 或 1.381966 < x ≤ 2 或 3 ≤ x < 3.618034 或 4.302776 < x ≤ 4.561553 Your problem has not been solved here? Please take a look at the hot problems !