SOLUTION: My question is |x-2| < 1/2 And I have to express this in interval notation. Any help would be great! thanks!

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Question 563088: My question is |x-2| < 1/2
And I have to express this in interval notation.
Any help would be great! thanks!

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Rules:

        If C is a positive number, then

  |Ax+B| < C           |             |Ax+B| > C 
                       |
is equivalent to       |          is equivalent to
                       |
 -C < Ax+B < C         |        Ax+B < -C  OR Ax+B > C

       [Same rules for < and >]

===================================================

 |x-2| < 1%2F2
 
is equivalent to

-1%2F2 < x-2 < 1%2F2

Multiply all three sides by 2

     -1 < 2x-4 < 1

Add 4 to all three sides:

  -1+4 < 2x-4+4 < 1+4
    
       3 < 2x < 5

Divide all three sides by 2

      3%2F2 < %282x%29%2F2 < 5%2F2

      3%2F2 < x < 5%2F2
    
Interval notation is

         (3%2F2, 5%2F2)


Edwin