Greetings all,

I am reviewing a limit question for a test and am trying to figure out the reason why it was solved as it was. Here is the question:

lim

x->4+

(4-x)|3x-14|

___________

|4-x|

Solution:

since x>4

(4-x)<0 (as x>4)

|3x-14|= 14-3x

|4-x|=x-4

(4-x) |3x-14|

___________

(x-4)

= -(14-3x)

=-2

I am confused as to why the |3x-14| becomes 14-3x. If the x is to be greater then 4, would |3x-14| be positive?

So in future questions with absolute values, should I first rewrite the absolute value (like in the x-4 case) so that it matches the situation (i.e. if x is less then or greater then a number, write it so that it factors that in?...is there an easier way to say that? :P)