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Different Types of Intervals in Inequality

If | x-3 | ...

Question

If $| x - 3 | < 2 x + 9$ , then $x$ lies in the interval

A

(- \infty, - 2)

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B

(- 2, 0)

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C

(- 2, \infty)

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D

(2, \infty)

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E

(- 12, - 2)

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Solution

The correct option is A $(- \infty, - 2)$
Given, $| x - 3 | < 2 x + 9$
$\Rightarrow - (2 x + 9) < x - 3 < 2 x + 9$
$\Rightarrow - 2 x - 9 < x - 3$ and $x - 3 < 2 x + 9$
$\Rightarrow - 3 x < 6$ and $- x < 12$
$\Rightarrow x > - 2$ and $x > - 12$
$\Rightarrow x > - 2$
Therefore, $x \in (- 2, \infty)$

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