Question 563088
<pre>
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 <u><</u> and <u>></u>]

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

 |x-2| < {{{1/2}}}
 
is equivalent to

{{{-1/2}}} < x-2 < {{{1/2}}}

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

      {{{3/2}}} < {{{(2x)/2}}} < {{{5/2}}}

      {{{3/2}}} < x < {{{5/2}}}
    
Interval notation is

         ({{{3/2}}}, {{{5/2}}})


Edwin</pre>