Find the range of \(x\).

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Find the range of \(x\).

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align} \dfrac{x-3}{x+5}\leq 0\hspace{.33em}\\~\\ \end{align}}\)
x has to be greater than -5 and smaller than or equal to 3 so that either top or bottom is negative (or that it is 0).
\(\Large -5

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numerator and denominator must be of opposite sign
We can see that \(x\neq-5\). Multiply both sides by \(x+5\), from here, split it into two cases. \[x-3\le0\quad \text{if }~~x+5>0\] \[x-3\ge0\quad \text{if }~~x+5<0\] For first case, you have \(x\le3\) if \(x>-5\), so range is \(-5
x belongs to (-5,3]
\(\LARGE x\in (-5,3]\)
hate notations, and love them
it feels good sometimes that I am capable of helping - not just asking questions. tnx, and yw

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