abs(x-1)-abs(x+1)+abs(2x+4)=8

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Solution for abs(x-1)-abs(x+1)+abs(2x+4)=8 equation:


Simplifying
abs(x + -1) + -1abs(x + 1) + abs(2x + 4) = 8

Reorder the terms:
abs(-1 + x) + -1abs(x + 1) + abs(2x + 4) = 8
(-1 * abs + x * abs) + -1abs(x + 1) + abs(2x + 4) = 8
(-1abs + absx) + -1abs(x + 1) + abs(2x + 4) = 8

Reorder the terms:
-1abs + absx + -1abs(1 + x) + abs(2x + 4) = 8
-1abs + absx + (1 * -1abs + x * -1abs) + abs(2x + 4) = 8
-1abs + absx + (-1abs + -1absx) + abs(2x + 4) = 8

Reorder the terms:
-1abs + absx + -1abs + -1absx + abs(4 + 2x) = 8
-1abs + absx + -1abs + -1absx + (4 * abs + 2x * abs) = 8
-1abs + absx + -1abs + -1absx + (4abs + 2absx) = 8

Reorder the terms:
-1abs + -1abs + 4abs + absx + -1absx + 2absx = 8

Combine like terms: -1abs + -1abs = -2abs
-2abs + 4abs + absx + -1absx + 2absx = 8

Combine like terms: -2abs + 4abs = 2abs
2abs + absx + -1absx + 2absx = 8

Combine like terms: absx + -1absx = 0
2abs + 0 + 2absx = 8
2abs + 2absx = 8

Solving
2abs + 2absx = 8

Solving for variable 'a'.

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

Reorder the terms:
-8 + 2abs + 2absx = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 2abs + 2absx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + abs + absx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + abs + absx)' equal to zero and attempt to solve: Simplifying -4 + abs + absx = 0 Solving -4 + abs + absx = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + abs + 4 + absx = 0 + 4 Reorder the terms: -4 + 4 + abs + absx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + abs + absx = 0 + 4 abs + absx = 0 + 4 Combine like terms: 0 + 4 = 4 abs + absx = 4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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