First, multiply each segment of the inequality by #color(red)(5)# to eliminate the fraction while keeping the system balanced:
#color(red)(5) xx -3 <= color(red)(5) xx (-4x + 3)/5 <= color(red)(5) xx 5#
#-15 <= cancel(color(red)(5)) xx (-4x + 3)/color(red)(cancel(color(black)(5))) <= 25#
#-15 <= -4x + 3 <= 25#
Next, subtract #color(red)(3)# from each segment of the inequality to isolate the #x# term while keeping the system balanced:
#-15 - color(red)(3) <= -4x + 3 - color(red)(3) <= 25 - color(red)(3)#
#-18 <= -4x + 0 <= 22#
#-18 <= -4x <= 22#
Now, divide each segment of the system by #color(blue)(-4)# to solve for #x# while keeping the system balanced. However, because we are multiplying or dividing by a negative term we must reverse the inequality signs:
#(-18)/color(blue)(-4) color(red)(>=) (-4x)/color(blue)(-4) color(red)(>=) 22/color(blue)(-4)#
#9/2 color(red)(>=) (color(blue)(cancel(color(black)(-4)))x)/cancel(color(blue)(-4)) color(red)(>=) -11/2#
#9/2 >= x >= -11/2#
