A carpenter is using a lathe to shape the final leg of a hand-crafted table. In order for the leg to fit, it needs to be 150 millimeters wide, allowing for a margin of error of 2.5 millimeters. Q: How can I write an absolute value inequality that models this relationship and find the range of widths that the table can be?
As I read the question, he wants the finished piece to be less than 150 mm. He will measure some amount, but the true measurement can be up to 2.5 mm greater than his measurement. What is the maximum measurement he can make and guarantee that the real size is less than 150 mm? Given that measurement, what is the minimum it could be?