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A "normal" temperature for a certain animal is 99.1 degrees F. If a temperature \( x \) that differs from the normal by at least 3.8 degrees F is considered unhealthy, write the condition for an unhealthy temperature \( x \) as an inequality involving an absolute value, and solve for \( x \).

Answer :

[tex]X[/tex] can indeed be unhealthy if it is whether[tex]x > = 102.9[/tex] and [tex]x = 95.3[/tex].

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The total kinetic velocity of all the molecules in a material is measured as temperature. A substance's average kinetic energy, temperature, and sensation of warmth increase with the rate at which its particles are moving.

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Generally speaking, the following thermometer values signify a fever: temporal artery, rectal, or ear temperature of at least 100.4 degrees Celsius. a minimum oral temperature of 100 F (37.8 C). 98 F (37.2 C) and higher in the crotch.

[tex]| x - 99.1 | > = 3.8[/tex]

To solve this inequality, we can consider two cases:

Case 1: [tex]x - 99.1 > = 3.8[/tex]

In this case, we have [tex]x > = 102.9[/tex], which means that the temperature is at least [tex]3.8[/tex] degrees above the normal temperature.

Case 2: [tex]x - 99.1 < = -3.8[/tex]

In this case, we have [tex]x < = 95.3[/tex], which means that the temperature is at least [tex]3.8[/tex] degrees below the normal temperature.

Therefore, an unhealthy temperature x can be either [tex]x > = 102.9[/tex] or[tex]x < = 95.3[/tex].

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Rewritten by : Barada

An unhealthy temperature for the animal is one that differs by at least 3.8°F from the normal temperature of 99.1°F. The inequality representing this is |x - 99.1| ≥ 3.8, which translates to x ≥ 102.9 or x ≤ 95.3. Temperatures outside these values are considered unhealthy.

To determine the condition for an unhealthy temperature for the animal, we need to write an inequality involving an absolute value. Given that a "normal" temperature for the animal is 99.1°F and any temperature that differs from this by at least 3.8°F is considered unhealthy, we start with the equation:

|x - 99.1| ≥ 3.8

Here, x represents the temperature of the animal. This inequality states that the absolute difference between the animal's temperature and the normal temperature of 99.1°F must be at least 3.8°F. To solve this, we'll break it down into two separate inequalities due to the properties of absolute values:

  1. x - 99.1 ≥ 3.8
  2. x - 99.1 ≤ -3.8

Solving the first inequality:

  1. x - 99.1 ≥ 3.8
  2. x ≥ 102.9

Solving the second inequality:

  1. x - 99.1 ≤ -3.8
  2. x ≤ 95.3

Therefore, the condition for an unhealthy temperature x is:

x ≥ 102.9 or x ≤ 95.3