The equation |x+1|=3 produces two solutions, x=2 and x=-4. ?

Question

For what values of a and b would the equation |x+a|=b produce two solutions that are equal. Explain your reasoning.

Answer 1

The reason that the two solutions are equal is because once you have evaluated the inner expression, you take the absolute vale of the terms. Absolute values are never negative (nonnegative integers), that is why the two solutions X = 2, X = -4 are equivalent.  With X = 2: 2+ 1 = 3, Ab. Val. = 3. With X = -4: -4 + 1 = -3, Ab. Val -3 = 3. Hope this helps.