SOLUTION: Please help me solve the following problem straigt from a worksheet: The equation |x+1|=3 produces two solutions, x=2 and x=-4. For what values of a and b would the equation |x+

Algebra ->  Absolute-value -> SOLUTION: Please help me solve the following problem straigt from a worksheet: The equation |x+1|=3 produces two solutions, x=2 and x=-4. For what values of a and b would the equation |x+      Log On


   

Question 155498: Please help me solve the following problem straigt from a worksheet:
The equation |x+1|=3 produces two solutions, x=2 and x=-4. For what values of a and b would the equation |x+a|=b produce two solutions that are equal? Explain your reasoning.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x+%2B+a%29+=+b
So
x+%2B+a+=+b+ and x+%2B+a+=+-b
Thus, the two solutions are
x+=+b-a and x+=+-b-a
In order to have the two solutions be the same,
b+-+a+=+-b+-+a
b+=+-b
Only b = 0 satisfies this.
x = -a, b = 0