How do you solve and graph #5-2x>=27#?

1 Answer
Mar 14, 2018

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(5)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#5 - color(red)(5) - 2x >= 27 - color(red)(5)#

#0 - 2x >= 22#

#-2x >= 22#

Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#(-2x)/color(blue)(-2) color(red)(<=) 22/color(blue)(-2)#

#(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) -11#

#x <= -11#

To graph this we will draw a vertical line at #-11# 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 left side of the line because the inequality operator also contains a "less than" clause:

graph{x <= -11 [-20, 20, -10, 10]}