First, expand the terms in parenthesis by multiplying each term in the parenthesis by the term outside the parenthesis:
#color(red)(2)(x - 4) > 5x + 1#
#(color(red)(2) xx x) - (color(red)(2) xx 4) > 5x + 1#
#2x - 8 > 5x + 1#
Next, subtract #color(red)(2x)# and #color(blue)(1)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-color(red)(2x) + 2x - 8 - color(blue)(1) > -color(red)(2x) + 5x + 1 - color(blue)(1)#
#0 - 9 > (-color(red)(2) + 5)x + 0#
#-9 > 3x#
Now, divide each side of the inequality by #color(red)(3)# to solve for #x# while keeping the inequality balanced:
#-9/color(red)(3) > (3x)/color(red)(3)#
#-3 > (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))#
#-3 > x#
We can state the solution in terms of #x# by reversing or "flipping" the entire inequality:
#x < -3#
