Answer to Question #217361 in Algebra for Kalery

Question

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

Answer 1

$$\dfrac{x^{1/2}(x-5)}{|x-7|}>0$$

$$x^{1/2}: x\geq0$$

$$|x-7|\not=0=>x\not=7$$

Then

$$x-5>0, x\not=0, x\not=7$$

The solution is

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

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