Question

Find all real solutions to the equation with absolute value
$-2|x+1|-2=4$

• A. $-4$
• B. no solutions
• C. $4$
• D. all real numbers
• E. $0$

Answer 1

The correct option is B no solutions

Since $|x|=x$ and $-x$, therefore,

$-2|x+1|-2=4$ may be calculated as:

$-2(x+1)-2=4$ and $2(x+1)-2=4$

$\Rightarrow -2x-2-2=4$ and $2x+2-2=4$

$\Rightarrow -2x=8$ and $2x=4$

$\Rightarrow x=-4$ and $x=2$

Since we have to find the real solutions with absolute value, therefore the equation has no solution.

Hence, option B is correct.