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.
T = 27±3
|T-27| <= 3
Surely you can figure the range.
So answer to b would be 24?
a) To represent this 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.
First, we split the inequality into two cases considering the positive and negative values:
Case 1: x - 27 ≤ 3
In this case, we solve for x by adding 27 to both sides:
x ≤ 30
Case 2: -(x - 27) ≤ 3
To solve for x in this case, we multiply both sides by -1 and distribute the negative sign:
-x + 27 ≤ 3
Subtract 27 from both sides:
-x ≤ -24
Divide both sides by -1, remembering to reverse the inequality:
x ≥ 24
Combining both cases, we find that the temperature range for the enclosure should be 24°C ≤ x ≤ 30°C.