Answer :
Sure, let's solve the problem step-by-step.
We need to write an absolute value inequality that represents the actual temperature varying between +7 degrees and -7 degrees from the set temperature of [tex]\(325^\circ F\)[/tex].
1. Understanding Variations:
The temperature can be 7 degrees higher or 7 degrees lower than the set temperature of [tex]\(325^\circ F\)[/tex]. Therefore, the actual temperature [tex]\(t\)[/tex] can range between [tex]\(325 + 7\)[/tex] and [tex]\(325 - 7\)[/tex].
2. Setting Up the Inequality:
We can express the actual temperature [tex]\(t\)[/tex] as:
[tex]\[
325 - 7 \leq t \leq 325 + 7
\][/tex]
Simplifying this, we get:
[tex]\[
318 \leq t \leq 332
\][/tex]
3. Using Absolute Value to Represent the Range:
Absolute value inequalities are useful for representing situations where the value can deviate by a certain amount from a central value. Here, [tex]\(t\)[/tex] is within 7 degrees of 325. This can be represented as:
[tex]\[
|t - 325| \leq 7
\][/tex]
Therefore, the absolute value inequality that correctly represents the temperature situation is:
[tex]\[
J. \, |t - 325| \leq 7
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\text{J. } |t - 325| \leq 7}
\][/tex]
We need to write an absolute value inequality that represents the actual temperature varying between +7 degrees and -7 degrees from the set temperature of [tex]\(325^\circ F\)[/tex].
1. Understanding Variations:
The temperature can be 7 degrees higher or 7 degrees lower than the set temperature of [tex]\(325^\circ F\)[/tex]. Therefore, the actual temperature [tex]\(t\)[/tex] can range between [tex]\(325 + 7\)[/tex] and [tex]\(325 - 7\)[/tex].
2. Setting Up the Inequality:
We can express the actual temperature [tex]\(t\)[/tex] as:
[tex]\[
325 - 7 \leq t \leq 325 + 7
\][/tex]
Simplifying this, we get:
[tex]\[
318 \leq t \leq 332
\][/tex]
3. Using Absolute Value to Represent the Range:
Absolute value inequalities are useful for representing situations where the value can deviate by a certain amount from a central value. Here, [tex]\(t\)[/tex] is within 7 degrees of 325. This can be represented as:
[tex]\[
|t - 325| \leq 7
\][/tex]
Therefore, the absolute value inequality that correctly represents the temperature situation is:
[tex]\[
J. \, |t - 325| \leq 7
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\text{J. } |t - 325| \leq 7}
\][/tex]
