We know that each Dixie cup holds 6 ounces of water.
There are 5 rows of meeting chairs with 10 chairs in each row, so there are a total of 5 * 10 = 50 chairs.
Bill fills one cup of water per chair, so he fills a total of 50 cups.
The total amount of water used is 50 * 6 = 300 ounces.
We are given that there are 128 ounces in a gallon, so the initial amount of water in the cooler is x gallons * 128 ounces/gallon = 128x ounces.
The amount of water left in the cooler after filling all the cups is 128x - 300 ounces.
We are given that the amount of water left in the cooler is 84 ounces, so we can write: 128x - 300 = 84.
Adding 300 to both sides, we get: 128x = 384.
Dividing both sides by 128, we get: x = 3.
The value of x is 3.
#### 3
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
While preparing for a meeting, Bill fills Dixie cups with water from out of a water cooler. The water cooler initially contains x gallons of water, and each Dixie cup holds 6 ounces of water.  If Bill fills one cup of water per each meeting chair, and there are 5 rows of meeting chairs with 10 chairs in each row, then how many ounces of water will be left in the cooler after all cups have been are filled? (There are 128 ounces in a gallon.)
If we know the answer to the above question is 84, what is the value of unknown variable x?

### Answer:
