Answer
All values of $x$ are a solution of this equation.
Work Step by Step
$|5x-2|=|2-5x|$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$5x-2=2-5x$ and $5x-2=-(2-5x)$
$\textbf{Solve the first equation:}$
$5x-2=2-5x$
Take $5x$ to the left side and $2$ to the right side:
$5x+5x=2+2$
$10x=4$
Solve for $x$:
$x=\dfrac{4}{10}$
$x=\dfrac{2}{5}$
$\textbf{Solve the second equation:}$
$5x-2=-(2-5x)$
$5x-2=5x-2$
$5x-5x=-2+2$
$0=0$
This equation is an identity. It is true for all values of $x$
All values of $x$ are a solution of this equation.
