How do you solve and graph #-n+6<7n+4#?

1 Answer
Nov 11, 2017

Answer:

See a solution process below:

Explanation:

First, add #color(red)(n)# and subtract #color(blue)(4)# from each side of the inequality to isolate the #n# term while keeping the inequality balanced:

#color(red)(n) - n + 6 - color(blue)(4) < color(red)(n) + 7n + 4 - color(blue)(4)#

#0 + 2 < color(red)(1n) + 7n + 0#

#2 < (color(red)(1) + 7)n#

#2 < 8n#

Now, divide each side of the inequality by #color(red)(8)# to solve for #n# while keeping the inequality balanced:

#2/color(red)(8) < (8n)/color(red)(8)#

#1/4 < (color(red)(cancel(color(black)(8)))n)/cancel(color(red)(8))#

#1/4 < n#

We can reverse or "flip" the entire inequality to state the solution in terms of #n#:

#n > 1/4#

To graph this we will draw a vertical line at #1/4# on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x> 1/4 [-2, 2, -1, 1]}