Answer :
Sure! Let's go through this problem step by step.
1. Understand the Initial Condition:
- We're told that the initial temperature of the oven is twice the room temperature. If we let [tex]\( x \)[/tex] represent the room temperature, then the oven's initial temperature is [tex]\( 2x \)[/tex].
2. Adjust the Temperature for Yeast Growth:
- Kevin knows that yeast thrives between [tex]\( 90^{\circ} F \)[/tex] and [tex]\( 95^{\circ} F \)[/tex]. He decreases the oven temperature by [tex]\( 44^{\circ} F \)[/tex] to get it within this range.
3. Set Up the Inequality:
- After Kevin reduces the temperature by [tex]\( 44^{\circ} F \)[/tex], the new temperature of the oven is [tex]\( 2x - 44 \)[/tex].
- We need to ensure this new temperature falls within the yeast's optimal range, which is between [tex]\( 90^{\circ} F \)[/tex] and [tex]\( 95^{\circ} F \)[/tex].
- Hence, we get the inequality:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
4. Interpret the Answer Choices:
- From the options provided, we see that only option B is the correct representation of the inequality we derived:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
Therefore, the correct inequality that represents the given situation is option B: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex].
1. Understand the Initial Condition:
- We're told that the initial temperature of the oven is twice the room temperature. If we let [tex]\( x \)[/tex] represent the room temperature, then the oven's initial temperature is [tex]\( 2x \)[/tex].
2. Adjust the Temperature for Yeast Growth:
- Kevin knows that yeast thrives between [tex]\( 90^{\circ} F \)[/tex] and [tex]\( 95^{\circ} F \)[/tex]. He decreases the oven temperature by [tex]\( 44^{\circ} F \)[/tex] to get it within this range.
3. Set Up the Inequality:
- After Kevin reduces the temperature by [tex]\( 44^{\circ} F \)[/tex], the new temperature of the oven is [tex]\( 2x - 44 \)[/tex].
- We need to ensure this new temperature falls within the yeast's optimal range, which is between [tex]\( 90^{\circ} F \)[/tex] and [tex]\( 95^{\circ} F \)[/tex].
- Hence, we get the inequality:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
4. Interpret the Answer Choices:
- From the options provided, we see that only option B is the correct representation of the inequality we derived:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
Therefore, the correct inequality that represents the given situation is option B: [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex].
