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mathmath333

  • one year ago

Find the range of \(x\).

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} \dfrac{x-3}{x+5}\leq 0\hspace{.33em}\\~\\ \end{align}}\)

  2. idku
    • one year ago
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    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).

  3. idku
    • one year ago
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    \(\Large -5<x\le 3 \)

  4. anonymous
    • one year ago
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    numerator and denominator must be of opposite sign

  5. geerky42
    • one year ago
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    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 \(-5<x\le3\) Second case is impossible.

  6. imqwerty
    • one year ago
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    x belongs to (-5,3]

  7. idku
    • one year ago
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    \(\LARGE x\in (-5,3]\)

  8. idku
    • one year ago
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    hate notations, and love them

  9. idku
    • one year ago
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    it feels good sometimes that I am capable of helping - not just asking questions. tnx, and yw

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