How do you solve and write the following in interval notation: #2< -3x + 2<=14#?

1 Answer
Apr 16, 2017

Answer:

See the entire solution process below:

Explanation:

First, subtract #color(red)(2)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#2 - color(red)(2) < -3x + 2 - color(red)(2) <= 14 - color(red)(2)#

#0 < -3x + 0 <= 12#

#0 < -3x <= 12#

Now, divide each segment by #color(blue)(-3)# to solve for #x# while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality operators:

#0/color(blue)(-3) color(red)(>) (-3x)/color(blue)(-3) color(red)(>=) 12/color(blue)(-3)#

#0 color(red)(>) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>=) -4#

#0 > x >= -4#

Or

#x < 0# and #x >= -4#

In interval notation [-4, 0)