To solve these equations, we need to isolate the variable "a".

For equation 1: (a-2)x = 2-a

First, distribute the x on the left side: ax - 2x = 2 - a

Next, add "a" to both sides: ax -2x + a = 2 - a + a

Simplify: ax - 2x + a = 2

Now, factor out the common factor on the left side: x(a - 2) = 2

Divide both sides by (a-2): x = 2/(a-2)

Therefore, the solution for equation 1 is x = 2/(a-2).

For equation 2: (a-2)x = a - 2

Proceed similarly:

ax - 2x = a - 2
ax - 2x - a = a - 2 - a
ax - 2x - a = - 2

Factor out common factor on the left side:

x(a - 2) = -2

Divide both sides by (a-2):

x = -2/(a-2)

Therefore, the solution for equation 2 is x = -2/(a-2).