{6,8,12,3,5,10-x,10+x,10} Given that the set of numbers has a unique mode, find the possible values of x.

The mode of a given set of values is one that is repeated
the most often. The values given are {6,8,12,3,5,10-x,10+x,10} and there is a unique
mode. I assume you are looking only for values of x such that the values in the set
remain positive.

Let's see which of the values satisfy the
fact that there is a unique mode. x =

0: this gives a
unique mode of 10

1: here the mode is not
unique

2: here also the mode is not
unique

3: here also the mode is not
unique

4: the mode is unique here,
6

5: the mode is unique here,
5

6: the mode is not unique

7:
the mode is unique, 3

8: the mode is not
unique

9: the mode is not
unique

10: the mode is not
unique

Therefore the values that x can take
are 0, 4, 5 and 7.