First, subtract #color(red)(1)# and add #color(blue)(8n)# to each side of the inequality to isolate the #n# term while keeping the inequality balanced:
#-color(red)(1) + 1 - 6n + color(blue)(8n) > -color(red)(1) - 7 - 8n + color(blue)(8n)#
#0 + (-6 + color(blue)(8))n > -8 - 0#
#2n > -8#
Now, divide each side of the inequality by #color(red)(2)# to solve for #n# while keeping the inequality balanced:
#(2n)/color(red)(2) > -8/color(red)(2)#
#(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) > -4#
#n > -4#
