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mathmath333
 one year ago
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mathmath333
 one year ago
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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0any short way to solve this . \(\large \color{black}{\begin{align} \left\dfrac{x^25x+4}{x^24}\right\leq 1\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \left\dfrac{x^25x+4}{x^24}\right = \left\dfrac{(x^24)5x+8}{x^24}\right = \left1+\dfrac{5x+8}{x^24}\right\) For this to be \(\le 1\), clearly we must have \[2\lt\dfrac{5x+8}{x^24}\lt 0\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0u mean \(\large \color{black}{\begin{align} 2\leq\dfrac{5x+8}{x^24}\leq 0\hspace{.33em}\\~\\ \end{align}}\) ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i am also confused on how to further solve this . \(\large \color{black}{\begin{align} 2\leq\dfrac{5x+8}{x^24}\leq 0\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Ahh yes, consider two cases : Case1 : \(x^24\gt 0\) multiply \(x^24\) through out and get \[2(x^24 )\le 5x+8 \le 0 \\~\\\implies 2x^2 \le 5x \le 8 \\~\\\implies 2x^2\ge 5x\ge 8 \\~\\\implies x\ge \frac{5}{2} \land x\ge \frac{8}{5}\\~\\\implies x\ge \frac{5}{2} \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1similarly you can work the other case i don't like this method yeah too boring

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[\large \color{black}{\begin{align} \left\dfrac{x^25x+4}{x^24}\right\leq 1\hspace{.33em}\\~\\ \end{align}}\] Since we have the absolute value, we need to consider two cases. One when we have an all positive problem like this \[\frac{x^25x+4}{x^24} \leq 1 \] or \[(\frac{x^25x+4}{x^24}) \leq 1 \] I'm going to try the all positive case \[\frac{x^25x+4}{x^24} \leq 1 \] so I would distribute the \[x^24 \] to the other side \[x^25x+4 \leq 1(x^24)\] \[x^25x+4 \leq x^24 \] \[x^25x+4 x^2+4 \leq 0\] (and then put everything on the left... combine like terms) \[x^2x^25x+4 +4 \leq 0\] \[5x+8 \leq 0\] (simplify and divide. since we have a negative number, the sign switches from \[\leq \] to \[\geq \] \[5x\leq 8\] \[x\geq \frac{8}{5}\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2there has got to be a way to make Latex nicer. this is ugly :P

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0the above needs to consider this two cases also \(\dfrac{x^25x+4}{x^24}\geq 0,\ \ \dfrac{x^25x+4}{x^24}< 0\)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2I said I just picked one case :P I'm aware that there are two.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0is there a way to transform the question in to this. \(\large \color{black}{\begin{align} \left\dfrac{x^25x+4}{x^24}+\color{black}{constant}\right\leq \color{red}{0}\hspace{.33em}\\~\\ \end{align}}\)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2maybe subtract that 1 on both sides? But I have never done it, so I don't know if it's a legal math move.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i m not saying substract \(1\) lol

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{x^2+5x4}{x^24} \leq 1\] \[x^2+5x4 \leq 1(x^24)\] \[x^2+5x4 \leq x^24\] \[x^2x^2+5x4+4 \leq 0\] \[2x^2+5x\leq 0\] \[x(2x+5)\leq 0\] x would be 0... blah don't want that case \[2x+5 \leq 0 \] \[2x \leq 5 \] \[x\geq \frac{5}{2} \] Looks like there is no faster way of doing this. You just have to use the absolute value rules which is consider the cases where we have an all positive situation and one where the negative sign is being distributed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why you have chosen 1 to subtract @UsukiDoll ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2We have two cases thanks to the absolute value remember we either have all positive or we have a negative sign attached to the problem and have to distribute it and then do the same process as above. @ganeshie8 had the same answers I have.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\(\color{blue}{\text{Originally Posted by}}\) @waterineyes Why you have chosen 1 to subtract @UsukiDoll ? \(\color{blue}{\text{End of Quote}}\) didn't do it.. just in case that move didn't make sense :P
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