How do you solve and graph #7-n<=19#?

1 Answer
smendyka
Nov 6, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(7)# from each side of the inequality to isolate the #n# term while keeping the inequality balanced:

#7 - color(red)(7) - n <= 19 - color(red)(7)#

#0 - n <= 12#

#-n <= 12#

Now, multiply each side of the inequality by #color(blue)(-1)# to solve for #n# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#color(blue)(-1) xx -n color(red)(>=) color(blue)(-1) xx 12#

#n color(red)(>=) -12#

To graph this we will draw a vertical line at #-12# on the horizontal axis.

The line will be a solid line because the inequality operator contains 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>=-12 [-20, 20, -10, 10]}

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