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### 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.