ian7777 wrote:

any algebraic equation with absolute value must be rewritten in its positive and negative form without the absolute value.

For example,

|x| = 6 so

x = 6 and x = -6

|x-3| = 5 becomes

x-3 = 5 and x-3 = -5 so

x=8 and x=-2, and both work when you plug them back in.

Same thing here.

Start with |b+6|-|b-5|=0, and make it

|b+6|=|b-5|

So b+6 = b-5 or b+6 = -(b-5)

Solve each one, and see that in the first one, b cancels and it's impossible, and in the second one, b=-.5

Taking time in to consideration, this will be the quickest method to solve the problem