What I don't understand, is if I have to multiply each side by the reciprocal how do I do it if the reciprocal is infinite like 3/4, which ends up being 1.3333333 etc. etc.
to obtain a reciprical, just switch the numerator and denominator.
the reciprical of 3/4 is 4/3
* the purpose of a reciprical is to get rid of any coefficients in front of your variable
so if you have 3/4 x -5 = 4
first you add 5 to both sides to get:
3/4 x = 9
now multiple by the reciprical of 3/4 which is 4/3
x = 12
try some practice problems...
find the reciprical of
NOTE: to find the recipricals of decimals you will first need to find its fractional equivalent.
the example you provided:
its fraction is 4/3.
now swithc numerator and denominator to get 3/4