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]
