Final answer:
The weight of a fountain pen must be within 10 grams ± 2 grams, represented as an absolute value inequality |w - 10| ≤ 2. This simplifies to the interval notation [8, 12], showing that the pens must weigh between 8 and 12 grams inclusive.
Step-by-step explanation:
The question asks us to write an absolute value inequality for the weight (w) of a fountain pen made in a factory. We know that the acceptable weight range is 10 grams ± 2 grams. Thus, the inequality can be written as |w - 10| ≤ 2. To solve this inequality:
- Split the absolute value inequality into two separate inequalities: w - 10 ≤ 2 and w - 10 ≥ -2.
- Solve each inequality for w: w ≤ 12 and w ≥ 8.
- Combine the solutions in interval notation: [8, 12].
This means the weight of each pen must be between 8 and 12 grams, inclusive.
When considering the measurement of an object, it is important to choose the appropriate metric unit. For a pencil, which weighs more than a paperclip but less than a kitten, the metric unit of grams is suitable. Similarly, calculating the total weight from a scale or subtracting weights in grams involves observing a scale and applying basic arithmetic operations.
In addition and subtraction of measurements, the answer should not have more decimal places than the least precise measurement used, which we see in examples with kilograms.