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Answer :
Sure, here is the detailed, step-by-step solution to the given problem.
We start with the inequality:
[tex]\[ 36.6 \leq \frac{5}{9}(F-32) \leq 37.5 \][/tex]
First, we need to replace [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex] using the formula [tex]\( C = \frac{5}{9}(F-32) \)[/tex]. This step is already done as provided.
Next, we multiply all three parts of the inequality by [tex]\( \frac{9}{5} \)[/tex]:
[tex]\[ \frac{9}{5} \cdot 36.6 \leq \frac{9}{5} \cdot \frac{5}{9}(F-32) \leq \frac{9}{5} \cdot 37.5 \][/tex]
Simplifying the middle term, we get:
[tex]\[ \frac{9}{5} \cdot \frac{5}{9}(F-32) = 1 \cdot (F-32) = F-32 \][/tex]
So, the inequality becomes:
[tex]\[ \frac{9}{5} \cdot 36.6 \leq F-32 \leq \frac{9}{5} \cdot 37.5 \][/tex]
Now, let's compute the left and right bounds:
[tex]\[ \frac{9}{5} \cdot 36.6 \][/tex]
[tex]\[ = 65.88000000000001 \][/tex]
And:
[tex]\[ \frac{9}{5} \cdot 37.5 \][/tex]
[tex]\[ = 67.5 \][/tex]
Thus, we have:
[tex]\[ 65.88000000000001 \leq F-32 \leq 67.5 \][/tex]
This concludes the step-by-step process to reach the solution provided.
We start with the inequality:
[tex]\[ 36.6 \leq \frac{5}{9}(F-32) \leq 37.5 \][/tex]
First, we need to replace [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex] using the formula [tex]\( C = \frac{5}{9}(F-32) \)[/tex]. This step is already done as provided.
Next, we multiply all three parts of the inequality by [tex]\( \frac{9}{5} \)[/tex]:
[tex]\[ \frac{9}{5} \cdot 36.6 \leq \frac{9}{5} \cdot \frac{5}{9}(F-32) \leq \frac{9}{5} \cdot 37.5 \][/tex]
Simplifying the middle term, we get:
[tex]\[ \frac{9}{5} \cdot \frac{5}{9}(F-32) = 1 \cdot (F-32) = F-32 \][/tex]
So, the inequality becomes:
[tex]\[ \frac{9}{5} \cdot 36.6 \leq F-32 \leq \frac{9}{5} \cdot 37.5 \][/tex]
Now, let's compute the left and right bounds:
[tex]\[ \frac{9}{5} \cdot 36.6 \][/tex]
[tex]\[ = 65.88000000000001 \][/tex]
And:
[tex]\[ \frac{9}{5} \cdot 37.5 \][/tex]
[tex]\[ = 67.5 \][/tex]
Thus, we have:
[tex]\[ 65.88000000000001 \leq F-32 \leq 67.5 \][/tex]
This concludes the step-by-step process to reach the solution provided.
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