First, multiply each side of the equation by the lowest common denominator for both fractions, #color(red)(14)#, to eliminate the fractions while keeping the equation balanced:

#color(red)(14)((X + 3)/2 - (X - 4)/7) = color(red)(14) xx 1#

#(color(red)(14) xx (X + 3)/2) - (color(red)(14) xx (X - 4)/7) = 14#

#(cancel(color(red)(14))7 xx ((X + 3))/color(red)(cancel(color(black)(2)))) - (cancel(color(red)(14))2 xx ((X - 4))/color(red)(cancel(color(black)(7)))) = 14#

#7(X + 3) - 2(X - 4) = 14#

#7X + 21 - 2X + 8 = 14#

#5X + 29 = 14#

#5X + 29 - color(red)(29) = 14 - color(red)(29)#

#5X + 0 = -15#

#5X = -15#

#(5X)/color(red)(5) = -15/color(red)(5)#

#(color(red)(cancel(color(black)(5)))X)/cancel(color(red)(5)) = -3#

#X = -3#