To determine whether a temperature [tex]\( x \)[/tex] is considered unhealthy based on its deviation from the normal human body temperature [tex]\( 98.6^{\circ} F \)[/tex], we need to assess how far [tex]\( x \)[/tex] is from [tex]\( 98.6 \)[/tex] degrees.
A temperature [tex]\( x \)[/tex] is considered unhealthy if it differs from the normal temperature by at least [tex]\( 2^{\circ} F \)[/tex]. This means the deviation should be more than [tex]\( 2^{\circ} F \)[/tex].
In mathematical terms, the absolute deviation of [tex]\( x \)[/tex] from [tex]\( 98.6 \)[/tex] can be expressed as:
[tex]\[ |x - 98.6| \][/tex]
We want this deviation to be more than [tex]\( 2^{\circ} F \)[/tex]. Therefore, the appropriate inequality should be:
[tex]\[ |x - 98.6| > 2 \][/tex]
This inequality states that the absolute difference between [tex]\( x \)[/tex] and [tex]\( 98.6 \)[/tex] must be greater than [tex]\( 2 \)[/tex] to be considered unhealthy.
Hence, the correct inequality to determine whether a temperature is unhealthy is:
[tex]\[ \boxed{|x - 98.6| > 2} \][/tex]
