The temperature on a thermostat is set to 72∘F, but the actual temperature can vary by as much as 2∘F. Let x represent the actual temperature to create an absolute value inequality to determine the range of possible-actual temperatures.
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Answers

Answer 1
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The Temperature On A Thermostat Is Set To 72F, But The Actual Temperature Can Vary By As Much As 2F.
Answer 2

Using an absolute value inequality, it is found that the range of temperatures is between 70ºF and 74ºF.

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The absolute value function measures the distance of a point to the origin, and is defined by:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

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The actual temperature is x, on a thermostat set to 72ºF. It can vary by as much as 2ºF, which means that the absolute value of the difference between x and 72 is at most 2, that is:

[tex]|x - 72| \leq 2[/tex]

Solving the inequality:

The term is both greater or equal to -2 and at most 2, thus:

[tex]x - 72 \geq >= -2[/tex]

[tex]x \geq 70[/tex]

And

[tex]x - 72 \leq 2[/tex]

[tex]x \leq 74[/tex]

Thus, the range of temperatures is between 70ºF and 74ºF.

A similar problem is given at https://brainly.com/question/24514895


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