The solution set for the inequality $(3 x - 6) (2 + x) < 0$ is:

{x : x < 2}

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{x : x > 2}

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{x : x > - 2}

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{x : x < - 2 o r x > 2}

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{x : - 2 < x < 2}

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Solution

The correct option is E ${x : - 2 < x < 2}$
Given, $(3 x - 6) (2 + x) < 0$
$\Rightarrow 6 x - 12 + 3 x^{2} - 6 x < 0$
$\Rightarrow 3 x^{2} - 12 < 0$
$\Rightarrow x^{2} - 4 < 0$
$\Rightarrow x^{2} < 4$
$\Rightarrow x < \pm 2$
Then $x : - 2 < x < 2$

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C

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