# If #2x- 5#, #x-1#, and #3x -8# are all integers and #x- 1# is the median of these integers, what is x?

##### 1 Answer

#### Explanation:

Note first that for all three values to be integers, we must have

Because

or

We consider each case.

**Case 1:**

Taken together, we have

**Case 2:**

If we go through the same steps as above with the directions of the inequalities reverse, we get

Having considered both cases, then, we have found the sole solution as