Describe how you know if an inequality is an “and” or an “or” problem. (use -3 < x+5 < 8). Also, how do you know if an absolute value question is an “and” or an “or” problem? Lastly, will you always have two solutions to an absolute value problem?

Answer 1

clearly the compound inequality is an and problem.

As for absolute value problems, think of the shape of the graph. It is a V shape. So, if |f(x)| < c, you have one interval, below the line y=c.

If |f(x)| > c, then you have the intervals outside the V, making it an or problem.

Of course, there may be other wrinkles, depending on the exact nature of f(x), but that's the idea.