1=abs(x+1)-abs(x-1)

Solution for 1=abs(x+1)-abs(x-1) equation:

Simplifying
1 = abs(x + 1) + -1abs(x + -1)

Reorder the terms:
1 = abs(1 + x) + -1abs(x + -1)
1 = (1 * abs + x * abs) + -1abs(x + -1)
1 = (1abs + absx) + -1abs(x + -1)

Reorder the terms:
1 = 1abs + absx + -1abs(-1 + x)
1 = 1abs + absx + (-1 * -1abs + x * -1abs)
1 = 1abs + absx + (1abs + -1absx)

Reorder the terms:
1 = 1abs + 1abs + absx + -1absx

Combine like terms: 1abs + 1abs = 2abs
1 = 2abs + absx + -1absx

Combine like terms: absx + -1absx = 0
1 = 2abs + 0
1 = 2abs

Solving
1 = 2abs

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2abs' to each side of the equation.
1 + -2abs = 2abs + -2abs

Combine like terms: 2abs + -2abs = 0
1 + -2abs = 0

Add '-1' to each side of the equation.
1 + -1 + -2abs = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2abs = 0 + -1
-2abs = 0 + -1

Combine like terms: 0 + -1 = -1
-2abs = -1

Divide each side by '-2bs'.
a = 0.5b-1s-1

Simplifying
a = 0.5b-1s-1