How do you simplify #-21\leq 5x - 9\leq 1#?

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Answer 1 · 2017-08-03T18:01:41

See a solution process below:

First, add #color(red)(9)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-21 + color(red)(9) <= 5x - 9 + color(red)(9) <= 1 + color(red)(9)#

#-12 <= 5x - 0 <= 10#

#-12 <= 5x <= 10#

Next, divide each segment by #color(red)(5)# to solve for #x# while keeping the system balanced:

#-12/color(red)(5) <= (5x)/color(red)(5) <= 10/color(red)(5)#

#-12/5 <= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) <= 2#

#-12/5 <= x <= 2#

Or

#x > -12/5#; #x <= 2#

Or, in interval notation:

#[-12/5, 2]#