Solve the inequations: x+5 x-3 <0 - Vidyadip

Question

Solve the inequations: $\frac{x+5}{x-3}<0$

✓

Answer

$
\frac{x+5}{x-3}<0
$
Since $\frac{a}{b}<0$, when $\mathrm{a}>0$ and $\mathrm{b}<0$ or $\mathrm{a}<0$ and $\mathrm{b}>0$
$\therefore$ either $x+5>0$ and $x-3<0$
or $x+5<0$ and $x-3>0$
Case l:
$
\begin{aligned}
& x+5>0 \text { and } x-3<0 \therefore x>-5 \text { and } x<3 \\
& \therefore-5<x<3 \\
& \therefore \text { solution set }=(-5,3) \\
& \text { Case II: } \\
& x+5<0 \text { and } x-3>0 \\
& \therefore x<-5 \text { and } x>3
\end{aligned}
$
Case II:
$
\begin{aligned}
& x+5<0 \text { and } x-3>0 \\
& \therefore x<-5 \text { and } x>3
\end{aligned}
$
which is not possible
$\therefore$ solution set $=\Phi$
$\therefore$ solution set of the given inequation is $(-5,3)$

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