A company makes boxes of crackers. These boxes are supposed to weigh 8 ounces with an error tolerance of 0.45 ounces. The acceptable weights for each box of crackers are modeled with the inequality shown below.
|x - 8| ≤ 0.45
The inequality representing the acceptable weights for each box of crackers is:
|w - 8| ≤ 0.45
This inequality states that the absolute value of the difference between the weight of each box of crackers (w) and 8 ounces should be less than or equal to 0.45 ounces.
To understand the inequality that models the acceptable weights for each box of crackers, we need to know the average weight of the boxes and the error tolerance.
In this case, the average weight of the boxes is 8 ounces, and the error tolerance is 0.45 ounces. The acceptable weights for each box of crackers can be modeled with an inequality. Let's call the weight of a box of crackers x.
The inequality that models the acceptable weights is:
| x - 8 | ≤ 0.45
Let's break down this inequality:
- The absolute value of (x - 8) represents the deviation from the average weight of 8 ounces.
- The ≤ symbol denotes that the deviation must be less than or equal to 0.45 ounces, as this is the accepted error tolerance.
To determine the acceptable weights, you can solve this inequality. Add 8 to both sides to eliminate the absolute value:
| x - 8 | + 8 ≤ 0.45 + 8
| x - 8 | ≤ 8.45
So, the acceptable weights for each box of crackers are the values of x that satisfy this inequality: | x - 8 | ≤ 8.45.