To address the question, we need to determine which inequality correctly represents the condition where a temperature [tex]\( x \)[/tex] is considered unhealthy if it differs from the normal body temperature [tex]\( 98.6^{\circ} F \)[/tex] by at least [tex]\( 2^{\circ} F \)[/tex].
1. Identify the Normal Temperature: The normal body temperature is [tex]\( 98.6^{\circ} F \)[/tex].
2. Determine the Condition for Unhealthiness: A temperature is considered unhealthy if the difference from the normal temperature is at least [tex]\( 2^{\circ} F \)[/tex]. This means the difference should be greater than or equal to [tex]\( 2^{\circ} F \)[/tex].
3. Express the Difference Mathematically:
- The difference between the temperature [tex]\( x \)[/tex] and the normal temperature [tex]\( 98.6^{\circ} F \)[/tex] is given by [tex]\( |x - 98.6| \)[/tex].
4. Formulate the Inequality:
- To represent the condition mathematically, we need the absolute value of the difference [tex]\( |x - 98.6| \)[/tex] to be greater than [tex]\( 2 \)[/tex]. This is because "at least" signifies that the smallest value it can be is [tex]\( 2 \)[/tex], and any value greater than [tex]\( 2 \)[/tex] is also acceptable.
- Therefore, the inequality that expresses this condition is:
[tex]\[
|x - 98.6| > 2
\][/tex]
Thus, the correct inequality to determine whether a temperature is considered unhealthy is:
B. [tex]\( |x - 98.6| > 2 \)[/tex]
So, the correct answer is [tex]\( 2 \)[/tex], representing option B.
