Translate the given statement into an algebraic inequality or compound inequality:
The tablet on a bottle of medicine states that the temperature, [tex]$t$[/tex], of the contents must be kept between [tex]$68^{\circ}$[/tex] and [tex]$77^{\circ}$[/tex] Fahrenheit.
a. [tex]$68>t>77$[/tex]
b. [tex]$68<t<77$[/tex]
c. [tex]$68 \geq t<77$[/tex]
d. [tex]$68 \leq t \leq 77$[/tex]
Please select the best answer from the choices provided
Answer (2)
The problem states that the temperature t must be between 6 8 ∘ and 7 7 ∘ Fahrenheit.
This means t must be greater than 68 and less than 77 .
The compound inequality that represents this is 68 < t < 77 .
Therefore, the correct answer is B .
Explanation
Understanding the Problem We need to translate the statement "The temperature, t , of the contents must be kept between 6 8 ∘ and 7 7 ∘ Fahrenheit" into an algebraic inequality. This means the temperature t must be greater than 6 8 ∘ F and less than 7 7 ∘ F.
Forming the Compound Inequality The inequality 68 < t means that t is greater than 68. The inequality t < 77 means that t is less than 77. Combining these two inequalities, we get 68 < t < 77 .
Selecting the Correct Option Comparing our compound inequality 68 < t < 77 with the given options, we see that it matches option b.
Final Answer Therefore, the correct answer is b. $68
The algebraic inequality representing the temperature requirements is 68 < t < 77 . This indicates that the temperature t must be greater than 68 degrees Fahrenheit and less than 77 degrees Fahrenheit. Therefore, the correct answer is option b.
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