First, subtract #color(red)(4)# from each segment of the inequality to isolate the #x# term while keeping the system of inequalities balanced:

#2 - color(red)(4) <= 4 - 3x - color(red)(4) < 7 - color(red)(4)#

#-2 <= 4 - color(red)(4) - 3x < 3#

#-2 <= 0 - 3x < 3#

#-2 <= -3x < 3#

Now, divide each segment of the inequality system by #color(blue)(-3)# to solve for #x# while keeping the system of inequalities balanced. However, remember, when dividing or multiplying an inequality by a negative number you must reverse the inequality terms:

#(-2)/color(blue)(-3) color(red)(>=) (-3x)/color(blue)(-3) color(red)(>) 3/color(blue)(-3)#

#2/3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>) -1#

#2/3 color(red)(>=) x color(red)(>) -1#