Answer
The equation is true for nonnegative numbers
$\quad (a\geq 0),$
and is false for negative numbers
$\quad (a\lt 0).$
Work Step by Step
The absolute value is defined as
$\quad |x|=\left\{\begin{array}{ll}
x, & x\geq 0\\
-x, & x \lt 0
\end{array}\right.$
Alternatively, as$\quad |x|=\sqrt{x^{2}.}$
Geometrically, on the number line, $|x|$ represents the distance (in units) from $x $ to $0.$
Note that $|x|$ can not be negative.
So, if the RHS of the given equation is negative
$\quad (a\lt 0)$,
the equation can not be true.
The equation stands true when RHS is nonnegative
$\quad (a\geq 0)$.
