Question

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

• A. $(-\infty ,-2)$
• B. $(-2,0)$
• C. $(-2,\infty )$
• D. $(2,\infty )$
• E. $(-12,-2)$

Answer 1

The correct option is A $(-\infty ,-2)$

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