Paul's Online Notes
Paul's Online Notes
Home / Algebra / Solving Equations and Inequalities / Absolute Value Inequalities
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 2.15 : Absolute Value Inequalities

3. Solve the following equation.

\[\left| {12x + 1} \right| \le - 9\] Show Solution

There is no solution to this inequality.

We know that absolute value will only give positive or zero answers and so this inequality is asking what values of \(x\) will give a value on the left side (after taking the absolute value of course) that is less than a -9. In other words, any solution requires that the absolute value give a negative number and we know that can’t happen. Therefore, there are no solutions to this inequality. This kinds of thing happens occasionally so don’t get too excited about it when it does.