The solution set of the rational inequality x + 9 x - 6 0 is

Question

The solution set of the rational inequality $\frac{x + 9}{x - 6} \leq 0$ is

Smart Achievers · Accepted Answer

(4)

We have, $\frac{x + 9}{x - 6} \leq 0$

Case I: $x + 9 \geq 0$ and $x - 6 < 0$

$\Rightarrow$ $x \geq - 9$ and $x < 6$ $\Rightarrow - 9 \leq x < 6$ $\dots (i)$

Case II: $x + 9 \leq 0$ and $x - 6 > 0$ $\Rightarrow x \leq - 9$ and $x > 6$

which is not possible simultaneously.

$∴$ Required solution set is $[- 9, 6)$ .

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