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
○ |323 + 50| = x
○ |x − 323| = 50
○ |x + 323| = 50

Explanation:

Step1: Understand absolute value for range

The absolute value equation \(|a - b| = c\) represents that \(a\) is within \(c\) units of \(b\). Here, \(x\) is the temperature of water, and it should be within 50 Kelvin of 323 Kelvin. So we need an equation where the difference between \(x\) (temperature) and 323 is 50 (the range).

Step2: Analyze each option

• Option 1: \(|323 - 50| = x\) calculates a specific value, not a range around 323.
• Option 2: \(|323 + 50| = x\) also calculates a specific value, not a range.
• Option 3: \(|x - 323| = 50\) means \(x\) is 50 units away from 323, which represents the range of temperatures (minimum and maximum) where water is liquid.
• Option 4: \(|x + 323| = 50\) would represent a range around -323, which doesn't make sense for water temperature.

Answer:

\(\boldsymbol{|x - 323| = 50}\) (the third option: \(|x - 323| = 50\))