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
