How many solutions does an absolute value inequality have???
Inequalities have the possibility of having infinite solutions, actually. It’s the range of solutions that matter. With that said, here is how you do them. 1) For an inequality in the form |z| < c, this translates to an AND. This translates to z < c AND z < -c, or, as a compound inequality, -c < z < c. The same holds true for less than or equal to. 2) For an inequality in the form |z| > c, this translates to an OR. This becomes z > c OR z < -c. Let's use these guidelines to solve your problem. |x + 6| >= 11 This obviously follows #2.
