Question

If $2|x+1{|}^2-|x+1|=3,$ then the sum of all real values of $x$ satisfying the equation is

• A. $2$
• B. $-2$
• C. $\frac{1}{2}$
• D. $-\frac{5}{2}$

Answer 1

The correct option is B $-2$

$2|x+1{|}^2-|x+1|=3$
$\Rightarrow 2|x+1{|}^2-|x+1|-3=0$
$\Rightarrow 2|x+1{|}^2+2|x+1|-3|x+1|-3=0$
$\Rightarrow (2|x+1|-3)(|x+1|+1)=0$
$\Rightarrow (2|x+1|-3)=0(\because |x+1|+1\ge 1)$
$\Rightarrow |x+1|=\frac{3}{2}$
$\Rightarrow x+1=\pm \frac{3}{2}$
$\Rightarrow x=\frac{1}{2},-\frac{5}{2}$
Sum $=-2$