Hi, there. I'm happy to help with this.

First of all, this is odd, because it's not a complete DS question. I assume it comes from something like:

Prompt: is x<3

one of the statements: |x|<3

Well, think about |x|<3. That means x is has a distance less than 3 from the origin. The solution to |x|<3 is the compound inequality -3 < x < 3. The value of x must be between -3 and 3. Of course, if x is anywhere in that range, it's less than 3, so this is sufficient.

The problem with pdshah's solution is: the proper word in the solution to that particular inequality is "and", not "or."

If |x|<3, then x<3 and -x<3 ==> x>-3. That gives us a narrow range on the number line that's a solution.

If the word were "or", and the solution x<3 or x>-3, that's the entire number line. Every real number is either less than 3 or greater than -3. Clearly, this inequality does not have a solution of all real numbers. That's why "or" is wrong.

Does that make sense? Please let me know if you have any further questions.

Mike