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Answer :
Sure! Let's go through the problem step by step to find the correct inequality that describes the situation:
1. Understand the Problem:
- The oven's initial temperature is twice the room temperature.
- The temperature is then decreased by 44°F to facilitate yeast growth, which thrives between 90°F and 95°F.
2. Define Variables:
- Let [tex]\( x \)[/tex] represent the room temperature.
- Therefore, the initial oven temperature = [tex]\( 2x \)[/tex].
3. Account for the Temperature Decrease:
- The temperature after decrease = [tex]\( 2x - 44 \)[/tex].
4. Set up the Inequality:
- The reduced temperature should be in the range where yeast thrives, which is between 90°F and 95°F:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
5. Choose the Correct Inequality from the Options:
- Let's compare our inequality with the options provided:
A. [tex]\( 90 \leq 2x + 44 \leq 95 \)[/tex]
B. [tex]\( 90 \geq 2x - 44 \leq 95 \)[/tex]
C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex] [tex]\(\leftarrow\)[/tex] This matches our derived inequality.
D. [tex]\( 90 \geq 2x + 44 \leq 95 \)[/tex]
6. Conclusion:
- The correct inequality is C: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex].
Therefore, the answer to the question is option C.
1. Understand the Problem:
- The oven's initial temperature is twice the room temperature.
- The temperature is then decreased by 44°F to facilitate yeast growth, which thrives between 90°F and 95°F.
2. Define Variables:
- Let [tex]\( x \)[/tex] represent the room temperature.
- Therefore, the initial oven temperature = [tex]\( 2x \)[/tex].
3. Account for the Temperature Decrease:
- The temperature after decrease = [tex]\( 2x - 44 \)[/tex].
4. Set up the Inequality:
- The reduced temperature should be in the range where yeast thrives, which is between 90°F and 95°F:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
5. Choose the Correct Inequality from the Options:
- Let's compare our inequality with the options provided:
A. [tex]\( 90 \leq 2x + 44 \leq 95 \)[/tex]
B. [tex]\( 90 \geq 2x - 44 \leq 95 \)[/tex]
C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex] [tex]\(\leftarrow\)[/tex] This matches our derived inequality.
D. [tex]\( 90 \geq 2x + 44 \leq 95 \)[/tex]
6. Conclusion:
- The correct inequality is C: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex].
Therefore, the answer to the question is option C.
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