First, multiply each side of the inequality by #color(red)(4)# to eliminate the fraction while keeping the inequality balanced:
#color(red)(4) xx (2 - 5x)/4 > color(red)(4) xx 3#
#cancel(color(red)(4)) xx (2 - 5x)/color(red)(cancel(color(black)(4))) > 12#
#2 - 5x > 12#
Next, subtract #color(red)(2)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-color(red)(2) + 2 - 5x > -color(red)(2) + 12#
#0 - 5x > 10#
#-5x > 10#
Now, divide each side of the inequality by #color(blue)(-5)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we need to reverse the inequality operator:
#(-5x)/color(blue)(-5) color(red)(<) 10/color(blue)(-5)#
#(color(blue)(cancel(color(black)(-5)))x)/cancel(color(blue)(-5)) color(red)(<) -2#
#x < -2#
