Answer :
Sure! Let's solve this problem step-by-step:
1. Initial Problem Information:
- The initial temperature is twice the room temperature. Let's denote the room temperature as [tex]\( x \)[/tex]. Therefore, the initial temperature is [tex]\( 2x \)[/tex].
- Kevin decreases this temperature by [tex]\( 44^\circ F \)[/tex].
2. Desired Temperature Range:
- The temperature needed for facilitating the yeast is between [tex]\( 90^\circ F \)[/tex] and [tex]\( 95^\circ F \)[/tex].
3. Setting up the Inequality:
- After Kevin decreases the initial temperature by [tex]\( 44^\circ F \)[/tex], the new temperature [tex]\( T \)[/tex] is given by:
[tex]\[
T = 2x - 44
\][/tex]
- This new temperature should be within the range needed for the yeast to work, so we can write the inequality as:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
4. Checking the Inequalities provided:
- A. [tex]\( 90 \leq 2x + 44 \leq 95 \)[/tex]
- This is incorrect as it suggests adding [tex]\( 44 \)[/tex] instead of subtracting.
- B. [tex]\( 90 \geq 2x - 44 \leq 95 \)[/tex]
- This incorrectly places an inequality sign after [tex]\( 90 \)[/tex].
- C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]
- This correctly represents our situation where [tex]\( 2x - 44 \)[/tex] is within the required range.
- D. [tex]\( 90 \geq 2x + 44 \leq 95 \)[/tex]
- This also incorrectly suggests adding [tex]\( 44 \)[/tex] and mixes inequality signs.
So, the correct inequality that represents the given situation is:
C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]
1. Initial Problem Information:
- The initial temperature is twice the room temperature. Let's denote the room temperature as [tex]\( x \)[/tex]. Therefore, the initial temperature is [tex]\( 2x \)[/tex].
- Kevin decreases this temperature by [tex]\( 44^\circ F \)[/tex].
2. Desired Temperature Range:
- The temperature needed for facilitating the yeast is between [tex]\( 90^\circ F \)[/tex] and [tex]\( 95^\circ F \)[/tex].
3. Setting up the Inequality:
- After Kevin decreases the initial temperature by [tex]\( 44^\circ F \)[/tex], the new temperature [tex]\( T \)[/tex] is given by:
[tex]\[
T = 2x - 44
\][/tex]
- This new temperature should be within the range needed for the yeast to work, so we can write the inequality as:
[tex]\[
90 \leq 2x - 44 \leq 95
\][/tex]
4. Checking the Inequalities provided:
- A. [tex]\( 90 \leq 2x + 44 \leq 95 \)[/tex]
- This is incorrect as it suggests adding [tex]\( 44 \)[/tex] instead of subtracting.
- B. [tex]\( 90 \geq 2x - 44 \leq 95 \)[/tex]
- This incorrectly places an inequality sign after [tex]\( 90 \)[/tex].
- C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]
- This correctly represents our situation where [tex]\( 2x - 44 \)[/tex] is within the required range.
- D. [tex]\( 90 \geq 2x + 44 \leq 95 \)[/tex]
- This also incorrectly suggests adding [tex]\( 44 \)[/tex] and mixes inequality signs.
So, the correct inequality that represents the given situation is:
C. [tex]\( 90 \leq 2x - 44 \leq 95 \)[/tex]
