Question

Solve the equation:

$\left|x-1\right|=1-x$

Answer 1

Solving the equation using function property :

$\left|x-1\right|=1-x$

$\left|x-1\right|=x-1$ for all $x\ge 1$

$\left|x-1\right|=-\left(x-1\right)$for all $x<1$

Case 1: When $x\ge 1$

$\left|x-1\right|=1-x$

$x-1=1-x$

$x+x=1+1$

$2x=2$

$x=1$

Case 2:When $x<1$

$\left|x-1\right|=1-x$

$-(x-1)=1-x$

$-x+1=1-x$

$1-x=1-x$

Here, the solution will be all the real values of $x$, which are less than $1$.
Therefore, the solution for $x$ is $(-\infty ,1]$