For an absolute value equation, there are two solutions. use the given equation and it’s solutions to algebraically prove this statement to be true |x|=9 (show work so i understand how to do it as well )

The first sentence is not true in general. Consider the equation . There are no solutions. Now consider . There is only one solution, .

But whatever. You're asked to demonstrate that has two solutions (which is true; the right hand side must be a positive integer in order to have two solutions). This follows immediately from the definition of absolute value, which says



So suppose . Then



Now suppose . Then



So two solutions to are .