Absolute value equation infinite solutions $$|3-x|+4x=5|2+x|-13$$
One of the solutions is $[3,\infty)$
I'm not familiar with interval solutions for absolute equations. 
How to solve for this interval?

One way to solve a problem like this is by graphing both sides of the equation.
You can do this in, for example, Desmos here. An image of the linked graph, showing that the two lines coincide for $x \geq 3$ (and showing that they coincidence at one other $x$-value, too):

Another way to solve these sorts of problems is by analyzing different cases: I see now that kingW3 has already provided an answer in this direction, so I'll curtail my response here. 
