True or false

For $|x|=y$ we have $x=\pm y$ So for $|x|=x$ we only have $\begin{aligned} \ x & = & x \\x & =& -x \end{aligned}$ But obviously , $x \neq -x$ So the answer is $\huge \boxed{False}$

The absolute value function $|x|$ can be defined as a piecewise function as below:

$|x| = \begin{cases} x &\quad x \geq 0\\ -x &\quad x < 0 \end{cases}$

From this definition, we can see clearly that $|x| = x$ only for all non-negative real $x$ .

Therefore, the statement given is $\boxed{\text{False}}$

$Let$

$x = -2$

$\left| -2 \right| =-2$

$\boxed{ 2\neq -2}$