Question

Find all real solutions to the equation with absolute value
$2|-2x+2|-3=13$

• A. $-5$
• B. $3$
• C. $5,-3$
• D. no solutions
• E. $0$

Answer 1

The correct option is C $5,-3$

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

therefore, $2|-2x+2|-3=13$ may be calculated as:

$2(-2x+2)-3=13$ and $-2(-2x+2)-3=13$

$\Rightarrow -4x+4-3=13$ and $4x-4-3=13$

$\Rightarrow -4x=12$ and $4x=20$

$\Rightarrow x=-3$ and $x=5$

Hence, option C is correct.