a) Do you remember what the definition of the mod function (absolute value function) is?

if and if .

So if then, by definition of a mod...

if and so if

AND

if , and so

if , thus if .

So your answer is right, but you have to write the restrictions on x as well as the solution set. The theorem you would have used here is the definition of a mod.

b) and c) follow the exact same principle.