Question 14649
There seems to be an error in your problem .There are 2 basic (inter-related)rules governing the dimensions of the 3 sides of a triangle for it to exist,that is for you to physically draw a triangle with those dimensions.They are 
 1. Sum of any 2 sides shall be greater than the third side and 
 2. Difference of any 2 sides  shall be less than the third side.
    Otherwise, what happens is that when you attempt to draw such a triangle , you will not be able to get the third vertex after having started with any 2 sides and 2 vertices.
    Hence ,in our present problem ,since 2 sides are 6 & 7 b,the third side x shall be greater than 13 or less than 1 (ofcourse it cannot be zero or negative).That is x should lie between 9 and 1 or should be greater than 13.
  Hence it is not correct to say that x has a maximum value .We can however say it has a minimum of zero in the lower range of number line and in that vicinity a local maximum of one and then again a minimum of 13 in the upper range of number line with no limit on maximum higher value beyond that.