# Absolute Value Inequality

• Jan 7th 2009, 07:33 PM
magentarita
Absolute Value Inequality
A tool and die shop makes a metal pull tab for a pop can. The length of the tab is 1.2 inches. The measurement may have an error of as much as 0.002 inches. Write an absolute value inequality that shows the range of the possible lengths of the tabs. Solve the inequality.
• Jan 8th 2009, 04:27 AM
HallsofIvy
Quote:

Originally Posted by magentarita
A tool and die shop makes a metal pull tab for a pop can. The length of the tab is 1.2 inches. The measurement may have an error of as much as 0.002 inches. Write an absolute value inequality that shows the range of the possible lengths of the tabs. Solve the inequality.

Since |x- 1.2| measures how much x differs from 1.2, that is just $|x- 1.2|\le 0.002$. That, of course, is the same as [tex]-0.002\le x- 1.2\le 0.002[tex] so $1.2- 0.002\le x\le 1.2+ 0.002$ or $1.198\le x\le 1.202$.
• Jan 9th 2009, 08:02 AM
magentarita
wow...
Quote:

Originally Posted by HallsofIvy
Since |x- 1.2| measures how much x differs from 1.2, that is just $|x- 1.2|\le 0.002$. That, of course, is the same as [tex]-0.002\le x- 1.2\le 0.002[tex] so $1.2- 0.002\le x\le 1.2+ 0.002$ or $1.198\le x\le 1.202$.

I would have never been able to come up with the answer.

Thanks