Question

Create an absolute value inequaility and solve for the following scenario: The target temperature for a well cooked piece of chicken is at most 165 degrees with a variance of 8 degrees. What range of temps could the chicken still be consumed? Use x as your variable.

Answer 1

To represent the absolute value inequality for the given scenario, we can use the absolute value of the difference between the target temperature and the actual temperature of the chicken. The absolute value ensures that we consider both higher and lower temperatures within the specified variance. Here's the inequality:

|x - 165| ≤ 8

In this inequality:

- "x" represents the actual temperature of the chicken.

- "165" is the target temperature.

- "8" is the variance.

To solve this inequality, we'll consider two cases: when (x - 165) is positive and when (x - 165) is negative.

Case 1: x - 165 is positive

x - 165 ≤ 8

Now, we'll solve for x:

x ≤ 165 + 8

x ≤ 173

Case 2: x - 165 is negative

-(x - 165) ≤ 8

Now, we'll solve for x:

-x + 165 ≤ 8

To isolate x, we'll subtract 165 from both sides:

-x ≤ 8 - 165

-x ≤ -157

Now, we'll multiply both sides by -1 to change the direction of the inequality. When you multiply or divide by a negative number, you flip the inequality sign:

x ≥ 157

So, the range of temperatures at which the chicken can still be consumed is:

157 ≤ x ≤ 173

This means the chicken can be consumed if its actual temperature falls within this range of 157 to 173 degrees Fahrenheit, considering the specified variance.

Explanation: