First, combine like terms on the left side of the equation:
#3n + 15 = 4 - 3 - n#
#3n + 15 = 1 - n#
Next, subtract #color(red)(15)# and add #color(blue)(n)# to each side of the equation to isolate the #n# term while keeping the equation balanced:
#3n + 15 - color(red)(15) + color(blue)(n) = 1 - n - color(red)(15) + color(blue)(n)#
#3n + color(blue)(n) + 15 - color(red)(15) = 1 - color(red)(15) - n + color(blue)(n)#
#3n + color(blue)(1n) + 0 = -14 - 0#
#(3 + color(blue)(1))n = -14#
#4n = -14#
Now, divide each side of the equation by #color(red)(4)# to solve for #n# while keeping the equation balanced:
#(4n)/color(red)(4) = -14/color(red)(4)#
#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -(2 xx 7)/color(red)(2 xx 2)#
#n = -(color(red)(cancel(color(black)(2))) xx 7)/color(red)(color(black)(cancel(color(red)(2))) xx 2)#
#n = -7/2#
