How do you solve #-6 ≤ 2 - 3m ≤ 7#?

1 Answer
Apr 21, 2018

Answer:

See a solution process below:

Explanation:

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

#-6 - color(red)(2) <= 2 - color(red)(2) - 3m <= 7 - color(red)(2)#

#-8 <= 0 - 3m <= 5#

#-8 <= -3m <= 5#

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

#(-8)/color(blue)(-3) color(red)(>=) (-3m)/color(blue)(-3) color(red)(>=) 5/color(blue)(-3)#

#8/3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))m)/cancel(color(blue)(-3)) color(red)(>=) -5/3#

#8/3 color(red)(>=) m color(red)(>=) -5/3#

Or

#m >= -5/3# and #m <= 8/3#

Or, in interval notation:

#[-5/3, 8/3]#