Question

A quality assurance engineer randomly checks manufactured parts to ensure that they are within 0.002 mm of the desired specifications. If the desired length of the part is 3 mm, then the compound inequality mc001-1.jpg represents the acceptable lengths. Choose the absolute value inequality that represents the situation.

Answer 1

Answer: 0.002 ≥ |x-3|

Step-by-step explanation:

Let the length of the part is x,

Since the Desired length is 3,

Also, the parts are within 0.002 mm of the desired specifications.

Thus, the maximum length of the part = 3 + 0.002

And, the minimum length of the part = 3 - 0.002

Therefore, we can write,

3 - 0.002 ≤ x ≤ 3 + 0.002

⇒ 3 - 0.002  ≤ x and x  ≤ 3 + 0.002

⇒ -0.002  ≤ x-3 and  x-3  ≤ 0.002

⇒ 0.002 ≥ -(x-3) and x-3 ≤ 0.002   (Because a > b ⇒ -a<-b)

⇒ 0.002 ≥ | x - 3 |

Which is the required absolute inequality.

Answer 2

|x - 3| ≤ 0.002 your answer should be A