First, subtract #color(red)(1.75x)# and add #color(blue)(1.75)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#color(blue)(1.75) - 0.25 + 1.75x - color(red)(1.75x) < color(blue)(1.75) - 1.75 + 2.25x - color(red)(1.75x)#
#1.5 + 0 < 0 + 0.5x#
#1.5 < 0.5x#
Now, divide each side of the inequality by #color(red)(0.5)# to solve for #x# while keeping the inequality balanced:
#1.5/color(red)(0.5) < (0.5x)/color(red)(0.5)#
#3 < (color(red)(cancel(color(black)(0.5)))x)/cancel(color(red)(0.5))#
#3 < x#
To state the solution in terms of #x# we can reverse or "flip" the entire inequality:
#x > 3#
