Absolute value and compound inequalities

Question

I have to write both types of equations for the following information, solve and then graph.

the temperature T of a refrigerator is at least 35°F and at most 41°F.

I do not understand how to do the absolute value but have come up with 35<T and T<41 for the compound value. Is this accurate?

Answer 1

Because the temp must be at least 35 then 35≤x.That is 35 is possible too.

Similarly, the temp is at most 41 means 41 is allowable so x ≤ 41.

This can be written as: 35 ≤ T ≤ 41.

To convert to absolute value consider what is the midpoint on the number line of the segment with endpoints 35 and 41? Just take the average. That number (38) is the same distance from 35 as it is from 41. That distance is 3. So any temp that satisfies the inequality must be less than 3 units from 38. This can be written as:

|T - 38 | ≤ 3.

If you were solving the above absolute value inequality you would write:

-3 ≤ T - 38 ≤ 3, then add 38 to all 3 parts of the compound inequality. 35 ≤ T ≤ 41. This confirms that the absolute value inequality is what we want.