Question 155554
THE EQUATION |X+1|=3 PRODUCES TWO SOULTIONS X=2 AND X=-4 FOR WHAT VALUES OF
A AND B WOULD THE EQUATION |X+A|=B PRODUCE TWO SOLUTIONS THAT ARE EQUAL.
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The two equations are:

X+A=B     and    X+A=-B
  X=B-A            X=-B-A

So the two solutions are B-A and -B-A.

We set those equal to each other:

      B-A=-B-A
      B+B=A-A
       2B=0
        B=0 

So the value of B would be 0.

Substitute in the original:

|X+A|=0

 X+A=0
   X=-A

So A can be any number, but B can only be 0.

and the one solution would always be X = -A

Edwin</pre>