1) A machine makes bolt that are 12 mm long. The bolts are considered acceptable if they are within 0.2 mm of 12 mm
Data:
length: 12 mm long
acceptance: +/- 0.2 mm of 12 mm
2) Question a: what is the longest the bolt cam be and still be accepatable?
Answer: 12 mm + 0.2 mm = 12.2 mm
3) Question b: what is the shortest the bold can be and still be acceptable?
Answer: 12 mm - 0.2 mm = 11.8 mm
4) Another machine is used to make 10 mm long bolts. For this machine, the bolts must have an error of less than 0.1 mm to be accepted. This can be represented by | x - 10 | < 0.1
5) Question a. write this inequality as a compound inequality without absolute bars:
Answer:
Remember | x - a | < b is equivalent to - b < x - a < b
Then:
- 0.1 < x - 10 < 0.1
6) Question b. solve the compound inequality:
Answer:
i) add 10 to each part of the inequality: - 0.1 + 10 < x - 10 + 10 < 0.1 + 10
ii) due the operations: 9.9 < x < 10.1
7) Question c. draw the solutions on a number line:
Answer:
-------o-----------------|----------------o----------
9.9 10 10.1
You must highlight the interval from 9.9 to 10.1 because that is the interval that contain the solutions.
The open dots are used to indicate that the extremes are not included. That is so because the signs of the inequality are <, which means that the limits are not included.
8) Question d. what do the solutions of the inequality mean for the bolt.
Answer:
The solution means that the lengths of the bolts must be greater than 9.9 and less than 10.1
