First step, multiply each side of the inequality by #color(red)(6)# to eliminate the fraction:
#color(red)(6) xx (2x - 4)/6 >= color(red)(6)(-5x + 2)#
#cancel(color(red)(6)) xx (2x - 4)/color(red)(cancel(color(black)(6))) >= (color(red)(6) xx -5x) + (color(red)(6) xx 2)#
#2x - 4 >= -30x + 12#
Next step, add the necessary terms from each side of the inequality to isolate the #x# terms on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced.
#2x - 4 + color(red)(4) + color(blue)(30x) >= -30x + 12 + color(red)(4) + color(blue)(30x)#
#2x + color(blue)(30x) - 4 + color(red)(4) >= -30x + color(blue)(30x) + 12 + color(red)(4)#
#(2 + 30)x - 0 >= 0 + 16#
#32x >= 16#
Last step, divide each side of the inequality by #color(red)(32)# to solve for #x# while keeping the inequality balanced:
#(32x)/color(red)(32) >= 16/color(red)(32)#
#(color(red)(cancel(color(black)(32)))x)/cancel(color(red)(32)) >= 1/2#
#x >= 1/2#
