Why the answer is E? [(x-1)^2 (3-x)^2] / (x+5) > 0

[AhmedAlmosuli]

 

[skeeter]

If [1,3] represents the closed interval [imath]1 \le x \le 3[/imath], I agree with choice D.

[imath]2 \in [1,3][/imath] and using that value, the inequality works out as [imath]\dfrac{1}{7} > 0[/imath] ... a true statement.

 

[Otis]

Why the answer is E?

Hi Ahmend. The answer is not E.

? If you know how to graph functions, then you could answer a lot of your own questions regarding misinformation in your materials.

Here's a partial graph of the Rational function, showing what happens within the interval (1,3).


It's clear that the function outputs positive values strictly in-between x=1 and x=3.
[imath]\;[/imath]

 

[Dr.Peterson]

View attachment 35263

Considering how often your book is wrong, you should change your questions from "Why is the answer E?" to "Please confirm that the book is wrong in saying the answer is E".

It's clear that you do better than the authors (or whoever writes the answers), so you should assume you are right.

I'm curious, though. Can you tell us exactly what "ÇK(SS)" means?

 

[skeeter]

Good job on plotting the critical values of x for the given inequality and a correct number line analysis.

 

[AhmedAlmosuli]

Considering how often your book is wrong, you should change your questions from "Why is the answer E?" to "Please confirm that the book is wrong in saying the answer is E".

It's clear that you do better than the authors (or whoever writes the answers), so you should assume you are right.

I'm curious, though. Can you tell us exactly what "ÇK(SS)" means?

The values that x can take, sorry I forgot to translate that

 

[Dr.Peterson]

The values that x can take, sorry I forgot to translate that

That's what I assumed; what I'm curious about is the notation. Does SS have a particular meaning, for example? Is ÇK the abbreviation of your word for "domain" or something?

Of course, I don't need to know this; I'm just interested in international variations of notation and terminology.

 

[Otis]

values that x can take

Hi. Variable x can take any value other than -5. Instead, I would expect that the exercise asks for the solution set (i.e., the set of x-values that produce a true statement).

I'm curious to know what the five circles represent on your diagram and why you'd subtracted 5 from 3 to the left of it.
[imath]\;[/imath]

 

[Dr.Peterson]

The values that x can take, sorry I forgot to translate that

I presume you mean "the values that x can take ... to make the inequality true"; and it's possible that SS means "solution set", if there is any English involved here. (I don't know why I used the word "domain" in my response, unless I was misdirected by your wording.)

I imagine that in your diagram

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the double circles mean that there is a double zero there (exponent 2), so the sign doesn't change. That could be a nice idea. But when I do this, I use a different symbol to represent a zero in the denominator (a point not in the domain), such as "u" for "undefined", so I know not to include that point even if the inequality includes equality.

 

[Otis]

the double circles mean that there is a double zero … That could be a nice idea.

Ah, yes. Haven't seen that noted, but I like it.

I use a different symbol to represent a zero in the denominator … such as "u"

I use Ø.
[imath]\;[/imath]