Expert: Steve Holleran - 8/15/2007

Question
QUESTION: Hii again! Can you help me find the absolute value of
 b+2 < -1?

Thanks.

ANSWER: Hi Emjade,

Well, you can do this one of two ways.

The first, and easiest, is to notice that the RESULT of an absolute value expression must always be zero or positive.  The stuff inside the a. v. can be positive, negative or zero, but not what comes out.  Therefore, there is no solution here, as abs(b+2) can't be <-1.  I has to be >= 0.

The longer way, which is how you would approach other absolute value problems is to split the expression in the a.v. into positive and negative cases:

Positive:   If (b+2) is positive, we can drop the a. v. symbols, and you have  b + 2 < -1 so b < -3.

Negative:   If (b+2) is negative, then its a. v. = -b - 2 and we have  -b - 2 < -1  so -b < 1 and b > -1.

Since this is a "less than" question, both of these have to be true:

         b < - 3    AND   b > -1

and you can see there is no solution.


I hope this works for you.

Steve Holleran

---------- FOLLOW-UP ----------

QUESTION: Could you also help me out  with this inequality?
-x+1 < -1/2

Answer
Hey Emjade,

Okay, I'm assuming this is not an absolute value.

First, subtract one from each side:

         -x + 1 - 1 < -1/2 - 1

         -x < -1 1/2

Now multiply through by (-1), and remember that you have to reverse the order sign:

         x > 1 1/2 or x > 3/2.

Let me know if it was supposed to be an a. v. problem, and I'll adjust the answer.

Steve Holleran