The average amount of water that a person drinks per day is 12 cups and differs by 3 cups. This ismodedeled by the equation |x-12|=3. Interpret the meaning of the solution to this equation.

Answer 1

The equation \(|x - 12| = 3\) represents the situations where the actual amount of water a person drinks (denoted by \(x\)) differs from the average amount (12 cups) by 3 cups.

To solve this equation, we can break it down into two separate equations:

1. \(x - 12 = 3\)
2. \(x - 12 = -3\)

Solving these:

1. For \(x - 12 = 3\): \[ x = 3 + 12 = 15 \]

2. For \(x - 12 = -3\): \[ x = -3 + 12 = 9 \]

Thus, the solutions to the equation \(|x - 12| = 3\) are \(x = 15\) and \(x = 9\).

Interpretation of the solution:

• \(x = 15\) means that one possible amount of water that a person can drink in a day is 15 cups, which is 3 cups more than the average.
• \(x = 9\) means that another possible amount of water a person can drink is 9 cups, which is 3 cups less than the average.

In summary, the solutions indicate that a person's daily water intake can vary from 9 cups to 15 cups, which shows that their intake deviates by 3 cups above or below the average of 12 cups.