Question
Solve the following inequalities and graph their solution set :
$\frac{2 x-5}{x+2}<2$
$\frac{2 x-5}{x+2}<2$
✓
Answer
The inequality $\frac{2 x-5}{x+2}<2$ is
eqivalent to $\frac{2 x-5}{x+2}-2<0 \Leftrightarrow \frac{2 x-5-2 x-4}{x+2}<0$
$\Rightarrow \frac{-9}{x+2}<0 $
$ \text { But } \frac{a}{b}<0, a<0$
$\Rightarrow b > 0$
Thus, $\frac{-9}{x+2}<0,-9<0$
$\Rightarrow x > -2 > 0$
$\Rightarrow x > -2$
The graph of this solution is $x > -2.$
eqivalent to $\frac{2 x-5}{x+2}-2<0 \Leftrightarrow \frac{2 x-5-2 x-4}{x+2}<0$
$\Rightarrow \frac{-9}{x+2}<0 $
$ \text { But } \frac{a}{b}<0, a<0$
$\Rightarrow b > 0$
Thus, $\frac{-9}{x+2}<0,-9<0$
$\Rightarrow x > -2 > 0$
$\Rightarrow x > -2$
The graph of this solution is $x > -2.$
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