Two numbers A and B are graphed on a number line. It is always, sometimes, or never true that A - |B| |B| Explain

Consider the cases when A is not > |B|:

In these cases " (A - |B| |B|) " is never true, because the second part of the proposition (sentence in " ") is not true.

So consider the cases when A>|B|

A is clearly positive, since |B| is positive.

case 1:

both A and B are positive, so |A|=A and |B|=B, and A>|B|,

in this case

A-|B|=A-B and clearly A-B
case 2:

B is negative, so |B|=-B,

thus A-|B|=A - (-B) = A+B

so A-|B|=A+B, thus A-|B| is not < A+B

case 3:

B=0,

A-|B|=A and A+B=A,

so A-|B|=A+B, thus A-|B| is not < A+B.

Answer: sometimes:

Precisely when A>B, and both A and B are positive.