Absolute Value Inequality: |x-0.3|≤ 0.0003 Solution Set: 2.9997≤ x≤ 3.0003
Practice makes perfect
We know the required width of the chain which is 0.3 inch. This is the midpoint of the range. We are asked to find the acceptable widths of the chain which is at most 0.0003 inch from the required width. This will be the maximum distance from the midpoint. Let's name the acceptable width as x and write the absolute valueinequality.
|x-0.3|≤ 0.0003
Now, because we know that our distance from the midpoint must be less than or equal to the given value, we can write an andcompound inequality.
- 0.0003 ≤ x-0.3 ≤ 0.0003
Finally, we can isolate x by adding 0.3 to all sides of the inequality.
2.9997 ≤ x ≤ 3.0003
The acceptable widths are between 2.9997 inches and 3.0003 inches.
