Some of the considerations (and being a tad out of touch with the exams these days, I am trying to fill in some gaps here) are -
(a) if you are moving items around to change a CG, then the envelope limits will be constant and the traditional formula is the easy way to find the answer
(b) if you are adding/removing ballast and the target CG is known (generally this will mean the limits are fixed) the traditional formula is the easy way to go (but there is no reason why you can't run the answer graphically .. with the caveat that accuracy may suffer depending on the graph used ..).
(c) if the limits are changing (typically the upper forward limit and, sometimes, the aft upper limit) then you are faced with simultaneous equations complicated by the need to account for second order moment equations in the slopey limit bits and perhaps the load line. This is a bit silly for pilot folk, so the way to approach this is to plot the incremental ballast moment on a moment by weight diagram of the envelope and read off the answer required. CAVEATS -
(i) on the moment (or IU) chart, the slopey CG bits are NOT straight lines, although they may be approximated as such on many charts
(ii) while most light aircraft load items have a linear moment equation, some don't .. this is seen often in the fuel load. In these latter cases, the answer will have an error, of some amount, if one approximates the non-linear line by a straight line (linearising) .. this is precisely what you are doing by plotting an incremental weight co-ordinate (weight, moment) and drawing a straight line between the start and finish points when the real line is a bit on the wavy or segmented side.
If you can post a bit more information, I can give you the appropriate engineering answers to specific questions.
Some of the earlier comments from others are a bit wide of the mark so I'll keep an eye on this thread ... as weight control, for my sins, is one of my bread and butter activities ...