To solve for this equation,

    6x+5 < 11 OR 3x-1 > 8

I would have to do the same to both sides correct? 
if I (-5) to the 11 side I must do the same to the 
8 side right? From there I would solve for x normally 
and that gives me the 2 answers? I think I have the
logic down, just need to make sure my steps are
correct. 
Thank you
-----------------------------------------------------

First of all that is a two-part inequality, not an
"equation".

Solve each part separately

6x + 5 < 11  OR  3x - 1 > 8
    -5   -5          +1  +1
----------------------------
6x     < 6   OR  3x     > 9

Divide both sides of first by 6
Divide both sides of second by 3

     x < 1   OR       x > 3 

Graph: Since x can be either
left of 1 or else right of 3, we
shade everwhere x can be: 

<==============o-----o==========>
  -3 -2 -1  0  1  2  3  4  5  6

Interval notation:   (-oo, 1) U (3, oo)

Edwin