Answer:To write an absolute value inequality that represents the acceptable range of candy pieces in a bag, we need to consider that the candy count can be up to 12 pieces above or below the typical count of 362.
Let's break it down step by step:
1. The typical count of candy pieces in a bag is 362.
2. The candy count can be up to 12 pieces above this number, which means the maximum count is 362 + 12 = 374.
3. The candy count can also be up to 12 pieces below the typical count, which means the minimum count is 362 - 12 = 350.
4. To represent the acceptable range of candy pieces in a bag using absolute value, we need to find the difference between the actual count and the typical count. We can then use the absolute value of this difference to set the acceptable range.
5. The absolute value of the difference between the actual count and the typical count should be less than or equal to 12. This ensures that the candy count falls within the acceptable range.
Putting it all together, the absolute value inequality that represents the acceptable range of candy pieces in a bag is:
|x - 362| ≤ 12
where x represents the actual count of candy pieces in the bag.
This inequality states that the absolute value of the difference between the actual count of candy pieces and the typical count of 362 should be less than or equal to 12. This means the candy count can range from 362 - 12 = 350 to 362 + 12 = 374.