# {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.

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### 1 Answer

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.**