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]#
