When solving systems of inequalities all operations perform on the system must be performed against each segment of the system:
First, multiply the system by #color(red)(5)# to eliminate the fraction:
#color(red)(5) xx -3 <= color(red)(5) xx (-3x + 4)/5 <= color(red)(5) xx 4#
#-15 <= cancel(color(red)(5)) xx (-3x + 4)/color(red)(cancel(color(black)(5))) <= 20#
#-15 <= -3x + 4 <= 20#
Next, subtract #color(red)(4)# from the system to isolate the #x# term:
#-15 - color(red)(4) <= -3x + 4 - color(red)(4) <= 20 - color(red)(4)#
#-19 <= -3x + 0 <= 16#
#-19 <= -3x <= 16#
Next, divide the system by #color(blue)(-3)# to solve for #x#/ However, because we are dividing or multiplying a system of inequalities by a negative term we must reverse the inequality signs.:
#(-19)/color(blue)(-3) color(red)(>=) (-3x)/color(blue)(-3) color(red)(>=) 16/color(blue)(-3)#
#19/3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>=) -16/3#
#19/3 >= x >= -16/3#
