Question

for water to be a liquid, its temperature must be within 50 kelvin of 323 kelvin. which equation can be used to determine the minimum and maximum temperatures between which water is a liquid?
|323 - 50| = x
|x - 323| = 50
|x + 323| = 50
|323 + 50| = x

Explanation:

Step1: Understand absolute value meaning

The absolute value equation \(|x - a| = b\) (where \(b\geq0\)) represents the set of numbers \(x\) that are \(b\) units away from \(a\) on the number line. Here, we want to find the temperatures \(x\) that are within 50 Kelvin of 323 Kelvin.

Step2: Analyze each option

• For \(|323 - 50| = x\): This just calculates the difference between 323 and 50, not related to finding \(x\) (the temperature) within 50 of 323.
• For \(|x - 323| = 50\): By the definition of absolute value, this equation means \(x - 323 = 50\) or \(x - 323=- 50\). Solving these gives \(x = 323 + 50\) (maximum temperature) and \(x=323 - 50\) (minimum temperature), which is exactly what we need to find the temperatures within 50 Kelvin of 323.
• For \(|x + 323| = 50\): This would represent numbers \(x\) that are 50 units away from - 323, not related to 323 Kelvin.
• For \(|323 + 50| = x\): This just calculates the sum of 323 and 50, not related to finding \(x\) (the temperature) within 50 of 323.

Answer:

\(|x - 323| = 50\)