Question

A certain machine operates properly when the relative humidity h satisfies the inequality -60 ≤ 21h - 50 ≤ 60. Solve for h to find the range of values for which the machine operates properly.

A) -5 ≤ h ≤ 5
B) 2 ≤ h ≤ 5
C) -5 ≤ h ≤ -2
D) -5 ≤ h ≤ 2

Answer 1

To solve the inequality -60 ≤ 21h - 50 ≤ 60, add 50 to all parts and then divide by 21, simplifying to get the range of –5/2 ≤ h ≤ 5 + 5/21. Hence, the machine operates properly when relative humidity h is between -5 and 5, which is Option A.

Step-by-step explanation:

The student has asked to solve the inequality –60 ≤ 21h – 50 ≤ 60 for the relative humidity h to find the range of values for which a machine operates properly. Let's solve the inequality step-by-step:

1. Add 50 to all three parts of the inequality: –60 + 50 ≤ 21h – 50 + 50 ≤ 60 + 50 which simplifies to –10 ≤ 21h ≤ 110.
2. Divide all three parts by 21 to isolate the variable h: –10/21 ≤ h ≤ 110/21.
3. Simplify the fractions to get the range of relative humidity: –5/2 ≤ h ≤ 5 + 5/21.

Since h must be an integer, the range of relative humidity is –5 ≤ h ≤ 5,

Therefore, the correct answer is Option A: –5 ≤ h ≤ 5