Question

The human body has a normal temperature of 98.6°F. Doctors will get worried if a sick patient has a temperature that varies from the normal by more than 3°F. Create an absolute value inequality and solve it to determine what body temperatures would be considered unhealthy.

Answer 1

`|T- 98.6| \geq 3`

And in order to solve this we have two possibilities:

Solution 1

`T -98.6 \leq -3`

And solving for T we got:

`T \leq 98.6- 3`

`T\leq 95.6`

Solution 2

And the other options would be:

`T -98.6 \geq 3`

`T \geq 101.6`

Explanation:

For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:

`|T- 98.6| \geq 3`

And in order to solve this we have two possibilities:

Solution 1

`T -98.6 \leq -3`

And solving for T we got:

`T \leq 98.6- 3`

`T\leq 95.6`

Solution 2

And the other options would be:

`T -98.6 \geq 3`

`T \geq 101.6`