The temperature of an enclosure for a pet snake should be about 27°C, give or take 3°C. (show your work)

a) What absolute value expression can be used to represent this situation?
b) Use the expression to determine the temperature range the enclosure should have.

a) To represent the situation, we can use the absolute value expression |x - 27| ≤ 3, where x represents the temperature of the enclosure.

b) To determine the temperature range the enclosure should have, we need to solve the absolute value inequality:

|x - 27| ≤ 3

There are two cases to consider:

Case 1: x - 27 ≥ 0
In this case, the absolute value expression simplifies to:
x - 27 ≤ 3

Solving for x:
x ≤ 27 + 3
x ≤ 30

So, if x - 27 is greater than or equal to 0, then the temperature of the enclosure should be less than or equal to 30°C.

Case 2: x - 27 < 0
In this case, the absolute value expression becomes:
-(x - 27) ≤ 3

Solving for x:
-x + 27 ≤ 3
27 ≤ x + 3
24 ≤ x

So, if x - 27 is less than 0, then the temperature of the enclosure should be greater than or equal to 24°C.

Combining both cases, we can determine the temperature range of the enclosure:
24°C ≤ x ≤ 30°C

Therefore, the temperature range the enclosure should have is between 24°C and 30°C.