Question

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

• A. $-2$
• B. $-2,0$
• C. $-1$
• D. no solution
• E. $0$

Answer 1

The correct option is E $0$

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

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

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

$\Rightarrow x=-2$ and $3x=0$

$\Rightarrow x=-2$ and $x=0$

Since we have to find the real solutions with absolute value, therefore $x=0$.

Hence option E is correct.