Chapter A.1, Problem 146AYU

To determine

To show:

a. A temperature of $97°\text{F}$ is unhealthy.

Answer to Problem 146AYU

a. $1.6\ge 1.5$

Explanation of Solution

Given:

Normal human body temperature is $98.6°\text{F}$. A temperature $x$ that differs from normal by at least $1.5°\text{F}$ is considered unhealthy. A formula that describes this is $\left|x-98.6\right|\ge 1.5$.

Calculation:

$\left|x-98.6\right|\ge 1.5$

a. $\left|97-98.6\right|\ge 1.5$

$\left|-1.6\right|\ge 1.5$

$1.6\ge 1.5$

A temperature of $97°\text{F}$ is unhealthy.

To determine

To show:

b. A temperature of $100°\text{F}$ is not unhealthy.

Answer to Problem 146AYU

b. $1.4<1.5$

Explanation of Solution

Given:

Normal human body temperature is $98.6°\text{F}$. A temperature $x$ that differs from normal by at least $1.5°\text{F}$ is considered unhealthy. A formula that describes this is $\left|x-98.6\right|\ge 1.5$.

Calculation:

$\left|x-98.6\right|\ge 1.5$

b. $\left|100-98.6\right|\ge 1.5$

$\left|1.4\right|\ge 1.5$

$1.4\ngeqq 1.5$

$1.4<1.5$

A temperature of $100°\text{F}$ is not unhealthy.