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Kevin is baking bread for a family function. The initial temperature of the oven is twice the room temperature. He knows that yeast, a key ingredient, thrives within the temperature range of [tex]$90^{\circ} F$[/tex] to [tex]$95^{\circ} F$[/tex]. To facilitate yeast growth, Kevin decreases the temperature of the oven by [tex]$44^{\circ} F$[/tex].

Which inequality represents the given situation?

A. [tex]$90 \leq 2x - 44 \leq 95$[/tex]
B. [tex]$90 \geq 2x - 44 \leq 95$[/tex]
C. [tex]$90 \geq 2x + 44 \leq 95$[/tex]
D. [tex]$90 \leq 2x + 44 \leq 95$[/tex]

Answer :

Sure! Let's solve this step-by-step to find the correct inequality.

1. Understand the Problem:
- Kevin's oven's initial temperature is twice the room temperature.
- Kevin decreases the oven temperature by [tex]\(44^\circ F\)[/tex] to ensure that the yeast thrives within a range of [tex]\(90^\circ F\)[/tex] to [tex]\(95^\circ F\)[/tex].

2. Set Up the Inequality:
- Let [tex]\(x\)[/tex] be the room temperature.
- Initially, the oven temperature is [tex]\(2x\)[/tex] (twice the room temperature).
- After decreasing the temperature by [tex]\(44^\circ F\)[/tex], the new oven temperature becomes [tex]\(2x - 44\)[/tex].

3. Establish the Range:
- You want this new temperature, [tex]\(2x - 44\)[/tex], to be between [tex]\(90^\circ F\)[/tex] and [tex]\(95^\circ F\)[/tex].

4. Write the Inequality:
- To represent this situation, the inequality should be:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]

This inequality ensures that after decreasing the temperature, it falls within the optimal range for the yeast to thrive.

Therefore, the correct inequality is option A: [tex]\(90 \leq 2x - 44 \leq 95\)[/tex].

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