4.01  Absolute Value Equations and Inequalties

Intermediate Algebra: One Step at a Time.  Page 306 - 314:   #25

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Dr. Robert J. Rapalje

Seminole Community College

Sanford, FL  32773

p. 308:  #25.         

Solution:  You know before you ever start this problem that it is a BETWEENNESS problem because:

1.    it has the absolute value sign,

2.    it has a “<” or “≤” symbol, and

3.    it is compared to a positive number 4. 

Now, you are probably asking, “Between what??”  So you need to find the ENDPOINTS.

The endpoints will be at:

                   and      

The solution for this inequality is the set of all values of x that are BETWEEN these endpoints, NOT including the endpoints.  On a number line, it looks like this:

 The final answer in interval notation (from LEFT to RIGHT!) is                 

                                      .

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