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)
The problem requires finding an equation that represents the temperature range for water to be a liquid, given it must be within 50 Kelvin of 323 Kelvin.
Define x as the temperature of the water.
Express the condition as an absolute value equation: ∣ x − 323∣ = 50 .
The equation ∣ x − 323∣ = 50 determines the minimum and maximum temperatures.
The equation that represents the condition is ∣ x − 323∣ = 50 .
Explanation
Understanding the Problem Let x be the temperature of the water in Kelvin. The problem states that for water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. This means the difference between the temperature x and 323 must be no more than 50. We can express this condition using an absolute value equation.
Formulating the Equation The absolute value equation that represents this condition is ∣ x − 323∣ = 50 . This equation states that the distance between x and 323 is equal to 50.
Solving the Absolute Value Equation To find the minimum and maximum temperatures, we can solve this absolute value equation. The equation ∣ x − 323∣ = 50 is equivalent to two separate equations:
x − 323 = 50
x − 323 = − 50
Finding Minimum and Maximum Temperatures Solving the first equation: x − 323 = 50 x = 323 + 50 x = 373
Solving the second equation: x − 323 = − 50 x = 323 − 50 x = 273
So, the minimum temperature is 273 Kelvin and the maximum temperature is 373 Kelvin.
Final Answer The equation that can be used to determine the minimum and maximum temperatures between which water is a liquid is ∣ x − 323∣ = 50 .
Examples
Absolute value equations are useful in many real-world scenarios. For example, in manufacturing, the dimensions of a product must be within a certain tolerance of the specified measurement. If a machine is set to produce parts that are 10 cm long, and the tolerance is 0.1 cm, then the actual length x of the part must satisfy the equation ∣ x − 10∣ ≤ 0.1 . This ensures that the parts produced are of acceptable quality. Similarly, in finance, absolute value can be used to model deviations from an expected return on investment.
