Q14. Solving Absolute Value Equations - Algebra 2

Question

FOOD 

For exercise 14-16, use the following information.

A meat thermometer is used to assure that a safe temperature has been reached to destroy bacteria. Most meat thermometers are accurate to within plus or minus $2{}^{\circ }F$

The ham you are baking needs to reach an internal temperature of $160{}^{\circ }F$. If the thermometer reads $160{}^{\circ }F$, write an equation to determine the least and greatest temperature of the meat.

Step-by-Step Solution

Answer

An equation with absolute value is $\left|x-160\right|=2$

Step 1 - Define Variable

Let the actual internal temperature of ham be $x{}^{\circ }F$

Step 2 - Meaning of given statement

Internal temperature of ham is $x{}^{\circ }F$

Temperature shown on thermometer is $160{}^{\circ }F$

Thermometer’s accuracy is $\pm 2{}^{\circ }F$

Step 3 - Write absolute value equation

As thermometer reads $160{}^{\circ }F$, so minimum temperature is $2{}^{\circ }F$ less than and maximum temperature is  $2{}^{\circ }F$ more than $160{}^{\circ }F$. Write it in equation form as shown below

$\begin{array}{c}x=160-2\text{ or }x=160+2\\ x-160=-2\text{ or }x-160=2\end{array}$

In absolute value equation it can be written as

$\left|x-160\right|=2$