Question

The weatherman announced that the temperature T over the next few weeks would be at least 64 F and at most 78 F. Write an absolute value inequality for the temperature over the next few weeks.

Answer 1

To write the absolute value inequality for the temperature over the next few weeks, use the average temperature and the difference between the average and the maximum temperature.

Step-by-step explanation:

To write an absolute value inequality for the temperature over the next few weeks, we can use the information provided that the temperature is at least 64 F and at most 78 F. Since the absolute value of a number is always non-negative, we can set up an inequality using the absolute value of the temperature minus a given constant.

Let T represent the temperature over the next few weeks. The absolute value inequality can be written as |T - 71| ≤ 7, where 71 is the average of 64 and 78, and 7 is the difference between 71 and the maximum temperature value (78).

This inequality represents that the temperature, T, is within 7 degrees of the average temperature, 71 F.