Question

|5x-9|=|x-2|

Answer 1

|5x-9|=|x-2|
|5x-9|= +x-2 OR |5x-9|=-x+2|
Will go with |5x-9|= +x-2 first.

Answer 2

|5x-9|= +x-2
+5x-9=+x-2 or -5x+9=+x-2
+5x-x=-2+9 or -5x-x=-2-9
4x=7 or -6x=-11
x=7/4 or x= 11/6

Now will go with |5x-9|=-x+2

Answer 3

I5x-9|=-x+2
5x-9=-x+2 or -5x+9=-x+2
5x+x=+2+9 or -5x+x=+2-9
6x=11 -4x=-7
x= 11/6 x=7/4

The answers are same

x=11/6 or 7/4

Answer 4

Basicaly when you have two absolute powers opposite to each other in these types of problems you can chose to just remove one of them, @dakota4340.
for example IxI=IaI
you can say that the problem is
IxI=a or that x=IaI
and the answers will be the same.

See in my work I just proved that!