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?
[tex]|323-50|=x[/tex]
[tex]|323+50|=x[/tex]
[tex]|x-323|=50[/tex]
[tex]|x+323|=50[/tex]
Answer (1)
Define the variable x as the temperature of the water.
Express the condition that the temperature must be within 50 Kelvin of 323 Kelvin using an absolute value equation: ∣ x − 323∣ = 50 .
The equation ∣ x − 323∣ = 50 represents the minimum and maximum temperatures for liquid water.
The correct equation is ∣ x − 323∣ = 50 .
Explanation
Setting up the equation Let x be the temperature of the water in Kelvin. The problem states that the temperature must be within 50 Kelvin of 323 Kelvin. This means the difference between x and 323 must be 50. We can express this using an absolute value equation.
Formulating the absolute value equation The absolute value equation that represents this situation is ∣ x − 323∣ = 50 . This equation states that the absolute difference between the temperature x and 323 is equal to 50. This will give us two possible temperatures: a minimum and a maximum.
Solving the equation and finding the temperature range To find the minimum temperature, we solve x − 323 = − 50 , which gives x = 323 − 50 = 273 . To find the maximum temperature, we solve x − 323 = 50 , which gives x = 323 + 50 = 373 . Therefore, the temperature must be between 273 K and 373 K. The equation ∣ x − 323∣ = 50 correctly represents the problem.
Examples
Understanding temperature ranges is crucial in many real-world applications. For example, in cooking, different ingredients and processes require specific temperature ranges to achieve the desired results. Similarly, in pharmaceuticals, maintaining precise temperature control is essential for the stability and efficacy of medications. This problem demonstrates how absolute value equations can be used to model and determine acceptable ranges in various scientific and practical contexts.
