Question 918816
Ambiguity is a problem.  Either equation can be good.  The professor should express the description without ambiguity, but did not.


"the difference of 9 and 3 times a number..."
Put into symbolism is this:
{{{abs(9-3x)}}}



Analyze the whole question further.
{{{highlight_green(abs(9-3x)=69)}}}.  THAT is what should be formed, based on the worded description.


If you want to solve that for x, you could first simplify, dividing left and right members by 3:


{{{(1/3)abs(9-3x)=69}}}
{{{abs(3-x)=23}}}
And from that, you have the two different cases,
{{{highlight(3-x=23)}}} {{{red(OR)}}}  {{{highlight(-(3-x)=23)}}}