To solve a system of inequalities whatever operation you perform on one segment of the system must be performed on all segments of the system.
First, add #color(red)(3)# to each segment of the system of inequalities to isolate the #x# term:
#6 + color(red)(3) <= -3x - 3 + color(red)(3) <= 12 + color(red)(3)#
#9 <= -3x - 0 <= 15#
#9 <= -3x <= 15#
Now, divide the system of inequalities by #color(blue)(-3)# to solve for #x#. However, because we are dividing or multiplying inequalities by a negative terms we must reverse the inequality signs:
#9/color(blue)(-3) color(red)(>=) (-3x)/color(blue)(-3) color(red)(>=) 15/color(blue)(-3)#
#-3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>=) -5#
#-3 >= x >= -5#
