SOLUTION: 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.

Algebra ->  Absolute-value -> SOLUTION: 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.      Log On


   

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

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