First, multiply each segment of the system of inequalities by #color(red)(25)# to eliminate the fractions while keeping the system balanced:
#color(red)(25) xx 1/25 < color(red)(25) xx (4 - 3x)/25 < color(red)(25) xx 4/5#
#25/25 < cancel(color(red)(25)) xx (4 - 3x)/color(red)(cancel(color(black)(25))) < cancel(color(red)(25)) 5 xx 4/color(red)(cancel(color(black)(5)))#
#1 < 4 - 3x < 20#
Next, subtract #color(red)(4)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#1 - color(red)(4) < 4 - 3x - color(red)(4) < 20 - color(red)(4)#
#-3 < 4 - color(red)(4) - 3x < 16#
#-3 < 0 - 3x < 16#
#-3 < -3x < 16#
Now, divide each segment of the system of inequalities by #color(blue)(-3)# to solve for #x# while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality terms:
#(-3)/color(blue)(-3) color(red)(>) (-3x)/color(blue)(-3) color(red)(>) 16/color(blue)(-3)#
#1 color(red)(>) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>) -16/3#
#1 > x > -16/3#
