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12. Assembly of a television in the factory is set at 45 minutes. The actual time required to assemble a television is shorter for some workers, while for others it is longer. However, each varies from the goal of 45 minutes by no more than 8 minutes. Which inequality below represents this scenario?

A. [tex]|t-8| \leq 45[/tex]
B. [tex]|t+8| \geq 45[/tex]
C. [tex]|2+45| \geq 8[/tex]
D. [tex]|t-45| \leq 8[/tex]



Answer :

GinnyAnswer
To solve this problem, let's break down the given information and find the appropriate inequality that represents the scenario.

1. Goal Time:
The time set for assembling a television is 45 minutes.

2. Variation Allowance:
The actual time required to assemble a television by different workers can vary from this goal time, but the variation is no more than 8 minutes.

This means the difference between the actual time \( t \) and the goal time of 45 minutes should be at most 8 minutes. To express this mathematically:

3. Absolute Value Inequality:
The absolute value function is used to represent the difference between two quantities without considering the sign. We want the absolute difference between the actual time \( t \) and the goal time 45 to be less than or equal to 8 minutes.

This can be written as:
[tex]\[ |t - 45| \leq 8 \][/tex]

This inequality states that the difference between the actual time \( t \) taken to assemble the television and the goal time (45 minutes) is at most 8 minutes.

Therefore, the correct inequality among the given options that represents this scenario is:
[tex]\[ |t - 45| \leq 8 \][/tex]

Hence, the answer is:
[tex]\[ |t - 45| \leq 8 \][/tex]

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