Question Video: Forming Absolute Value Inequalities to Model a Real-Life Situation Mathematics • Second Year of Secondary School

Video Transcript

The tolerance for a ball bearing is 0.01. If the diameter is required to be 2.0 inches and the measured value of the diameter is 𝑥 inches, express the acceptable values of 𝑥 using absolute value notation.

Let’s think about what we know. We have a required diameter of two inches and a tolerance of 0.01. And that means the lower bound of our 𝑥-value would be two inches minus the 0.01 tolerance. And our upper bound would be 2.0 plus the 0.01 tolerance. We have a range of 𝑥-values from 1.99 to 2.01. But how do we write this in absolute value notation?

We need to be able to say the distance from 𝑥 to two must be less than or equal to the tolerance of 0.01. We can model this with absolute value by saying the absolute value of 𝑥 minus 2.0 must be less than or equal to 0.01.