Explain why there is no solution to the inequality |w - 2| + 5

Question

Explain why there is no solution to the inequality |w - 2| + 5 < 3.

jamesj · Answer

Notice first that
|w - 2| + 5 < 3
implies that
|w - 2| < -2

Now the question is, can the absolute value of anything be less than -2?  

Is there any number x such that |x| < -2?  Or that |x| = -2?

jamesj · Answer

For example
x = 2 then |x| = 2
x =-2 then |x| = 2

So what number |x|  is there such that |x| = -2?

jamesj · Answer

The answer is there no such number.  Now the question for you is why.  Once you know the answer to that you wil know the answer to your problem too.

If you're stuck, go back to the definition of absolute value.