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  4. If |x - 3| < 2x + 9 then x lies in the interval

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

KEAMKEAM 2015Linear Inequalities

Solution:

$|x-3| < 2 x+9$
$\Rightarrow -(2 x+9) < x-3<2 x+9$
$\Rightarrow -2 x-9 < x-3$
and $x-3<2 x+9$ < br/>
$\Rightarrow -3 x<6$ and $-x < 12$
$\Rightarrow x>-2$ and $x > -12$
$\Rightarrow x > -2$
$\therefore x \in(-2, \infty)$