A bottling company is filling 32 oz bottles of water. A bottle is accepted if it contains between 32.85 and 31.15 oz of water. What absolute value inequality describes the tolerance of volume of water in the bottle?

midway between the two extremes is (32.85+31.15)/2 = 32.00

So, |x-32.00| <= 0.85

thank you

To find the absolute value inequality that describes the tolerance of volume of water in the bottle, we need to consider the acceptable range around the desired volume of 32 ounces.

Let's start by finding the midpoint of the acceptable range. The midpoint is the average of the upper limit (32.85 oz) and the lower limit (31.15 oz):

Midpoint = (32.85 + 31.15) / 2 = 64 / 2 = 32 oz

Now, we can determine the difference between the desired volume (32 oz) and the midpoint:

Difference = 32 - 32 = 0

Since the difference is 0, the absolute value inequality will be in the form:

|volume - midpoint| ≤ difference

Substituting the values in, we get:

|volume - 32| ≤ 0

However, any absolute value of a real number is always greater than or equal to zero. Therefore, the absolute value inequality simplifies to:

volume - 32 = 0

Which further simplifies to:

volume = 32

Therefore, the absolute value inequality that describes the tolerance of volume of water in the bottle is:

|volume - 32| ≤ 0