First, group and then combine like terms on the right side of the inequality:
#0 < -3N + 6 - 12N#
#0 < -3N - 12N + 6#
#0 < (-3 - 12)N + 6#
#0 < -15N + 6#
Next, subtract #color(red)(6)# from each side of the inequality to isolate the #N# term while keeping the inequality balanced:
#0 - color(red)(6) < -15N + 6 - color(red)(6)#
#-6 < -15N + 0#
#-6 < -15N#
Now, divide each side of the inequality by #color(blue)(-15)# to solve for #N# while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative term we must reverse the inequality operator:
#(-6)/color(blue)(-15) color(red)(>) (-15N)/color(blue)(-15)#
#(-3 xx 2)/color(blue)(-3 xx 5) color(red)(>) (color(blue)(cancel(color(black)(-15)))N)/cancel(color(blue)(-15))#
#(color(blue)(cancel(color(black)(-3))) xx 2)/color(blue)(color(black)(cancel(color(blue)(-3))) xx 5) color(red)(>) N#
#2/5 > N#
To state the solution in terms of #N# we can reverse or "flip" the entire inequality:
#N < 2/5#
