How do you solve and graph #−44> −2x − 8 ≥ −8#?

1 Answer
Feb 7, 2017

Answer:

See the entire solution process below:

Explanation:

To solve a system of inequalities you need to perform each operation across the entire system to keep the system of inequalities balanced. First, we will add #color(red)(8)# to each segment of the inequality:

#-44 + color(red)(8) > -2x - 8 + color(red)(8) >= -8 + color(red)(8)#

#-36 > -2x - 0 >= 0#

#-36 > -2x >= 0#

Now, we will divide each segment of the system by #color(blue)(-2)# to solve for #x#. However, because we are multiplying or dividing by a negative term we must reverse the inequality signs:

#(-36)/color(blue)(-2) color(red)(<) (-2x)/color(blue)(-2) color(red)(<=) 0/color(blue)(-2)#

#18 color(red)(<) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) 0#

#18 < x <= 0#