Answer to Question #217361 in Algebra for Kalery

Question #217361

The solutions to the inequality ( [(x1/2)(x-5)] / lx-7l )>0 are all the x elements of R such that?


A. x>0 and x


1
Expert's answer
2021-08-11T19:22:19-0400
x1/2(x5)x7>0\dfrac{x^{1/2}(x-5)}{|x-7|}>0

x1/2:x0x^{1/2}: x\geq0

x70=>x7|x-7|\not=0=>x\not=7

Then


x5>0,x0,x7x-5>0, x\not=0, x\not=7

The solution is


x(5,7)(7,)x\in(5, 7)\cup(7, \infin)

The statement that the solutions to the inequality x1/2(x5)x7>0\dfrac{x^{1/2}(x-5)}{|x-7|}>0 are all the xx elements of R\R  is False.




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