First, subtract #color(red)(7)# from each side of the inequality to isolate the #n# terms while keeping the inequality balanced:
#3n + 7 - color(red)(7) - 7n < -5 - color(red)(7)#
#3n + 0 - 7n < -12#
#3n - 7n < -12#
Next, combine like terms on the left side of the inequality:
#(3 - 7)n < -12#
#-4n < -12#
Now, divide each side of the inequality by #color(blue)(-4)# to solve for #n# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must revers the inequality operator:
#(-4n)/color(blue)(-4) color(red)(>) (-12)/color(blue)(-4)#
#(color(red)(cancel(color(black)(-4)))n)/cancel(color(blue)(-4)) color(red)(>) 3#
#n > 3#
