Using lists handles multiple observations. Look in the online documentation about lists, set ("="), set delayed (":="), and Solve. If you have a specific example about the use of Solve (including in code you've attempted), then I think the Community could give you a lot of assistance. Looking at "Core Language & Structure" in the Documentation Center is also highly recommended.

My recommendation is to avoid subscripts (now and maybe forever). If I understand what you want, the code can be written as:

\[Epsilon]L = -5;
\[Epsilon]H = -\[Epsilon]L;
\[Epsilon] = UniformDistribution[{\[Epsilon]L, \[Epsilon]H}]
g[x_] := PDF[\[Epsilon], x]

and

 g[z]
 g[3.5]
 g[50]

results in