First, we need to convert the mixed number to a fraction:

#16.7 < 3(x + 4 1/2)#

#16.7 < 3(x + [4 + 1/2])#

#16.7 < 3(x + [(4 xx 2/2) + 1/2])#

#16.7 < 3(x + [8/2 + 1/2])#

#16.7 < 3(x + 9/2)#

#16.7 < 3(x + 4.5)#

Next, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#16.7 < color(red)(3)(x + 4.5)#

#16.7 < (color(red)(3) xx x) + (color(red)(3) xx 4.5)#

#16.7 < 3x + 13.5#

Then, subtract #color(red)(13.5)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#16.7 - color(red)(13.5) < 3x + 13.5 - color(red)(13.5)#

#3.2 < 3x + 0#

#3.2 < 3x#

Now, divide each side of the inequality by #color(red)(3)# to solve for #x# while keeping the inequality balanced:

#3.2/color(red)(3) < (3x)/color(red)(3)#

#1.0bar6 < (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))#

#1.0bar6 < x#

We can state the solution in terms of #x# by reversing or "flipping" the entire inequality:

#x > 1.0bar6#