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How to solve this inequality?

I'm grateful for all and any replies.

I attached the inequality and the purported solution in an image, as I determined it'd be easier than figuring out the formatting in this site.

I'm really at a loss. I've tried solving it numerous times, thought I had it a couple, and haven't actually gotten anywhere.

Re: How to solve this inequality?

Hola :)

Esa inecuación es equivalente a:

YO particularmente lo resuelvo así:

https://hhs1xw.blu.livefilestore.com...uacionesxd.png

PS: Lo siento, resolví el problema para , como es , simplemente no toma el -5, -3 y -8, así que es abierto en esos puntos:

Re: How to solve this inequality?

This can be done qualitatively. First lets identify our domain. Where is the denominator equal to 0 ?, at points 0, 5, 7. So I got D = . Now lets since the inequality > 0, the numerator cannot be zero also. So where is the numerator 0? I got -2, 8, -3, 10, -5. So our set of possible solutions consists of .

Now consider any . We see that the denominator > 0. So, the numerator must also be > 0, So only consider odd power terms in numerator, since even power gives positive no matter what. So take , since we see , it must be that (negative * negative = positive) . Which means either OR which means OR ., the second is impossible, x cannot be > 3 and < -5 at the same time.. So x \in

Now we solved what happens when we got for the inequality holds. Now assume We only need to consider because every other term evaluates to positive. So for One option is for both num and denom to be positive. which gives which is not possible. So it must be that both num and denom are negative. so that means which gives us which gives us the interval . So for the inequality holds in . So our soln is