Tolerances In quality control and other applications, we often wish to keep the difference...

Tolerances In quality control and other applications, we often wish to keep the difference between two quantities within some predetermined amount, or tolerance. For example, suppose y = 2x + 1 and we want y to be within 0.01 unit of 4. This criterion can be written as | y − 4 | < |.01. To find the values of x that satisfy this condition on y, we use properties of absolute value as follows.

Keeping x in the open interval (1.495, 1.505) will ensure that the difference between y and 4 is less than 0.01. In Exercises find the open interval in which x must lie in order for the given condition to hold

y = 4x − 8, and the difference between y and 3 is less than 0.001.