How do you solve #0<-3N +6 - 12N#?

1 Answer
Apr 23, 2017

Answer:

See the entire solution process below:

Explanation:

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#