First, subtract #color(red)(2)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#-3 - color(red)(2) <= 2 - color(red)(2) - 2x <= 9 - color(red)(2)#
#-5 <= 0 - 2x <= 7#
#-5 <= -2x <= 7#
Net, divide each segment by #color(blue)(-2)# to solve for #x# while keeping the system balanced. However, because we are dividing or multiplying inequalities by a negative number we must reverse the inequality operators:
#(-5)/color(blue)(-2) color(red)(>=) (-2x)/color(blue)(-2) color(red)(>=) 7/color(blue)(-2)#
#5/2 color(red)(>=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>=) -7/2#
#5/2 color(red)(>=) x color(red)(>=) -7/2#
Or
#x >= -7/2#; #x <= 5/2#
Or, in interval notation:
#[-7/2, 5/2]#
