Abs(x-1)+abs(x+2)+abs(x+3)=0

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Solution for Abs(x-1)+abs(x+2)+abs(x+3)=0 equation:


Simplifying
Abs(x + -1) + abs(x + 2) + abs(x + 3) = 0

Reorder the terms:
bsA(-1 + x) + abs(x + 2) + abs(x + 3) = 0
(-1 * bsA + x * bsA) + abs(x + 2) + abs(x + 3) = 0
(-1bsA + bsxA) + abs(x + 2) + abs(x + 3) = 0

Reorder the terms:
-1bsA + bsxA + abs(2 + x) + abs(x + 3) = 0
-1bsA + bsxA + (2 * abs + x * abs) + abs(x + 3) = 0
-1bsA + bsxA + (2abs + absx) + abs(x + 3) = 0

Reorder the terms:
-1bsA + bsxA + 2abs + absx + abs(3 + x) = 0
-1bsA + bsxA + 2abs + absx + (3 * abs + x * abs) = 0
-1bsA + bsxA + 2abs + absx + (3abs + absx) = 0

Reorder the terms:
2abs + 3abs + absx + absx + -1bsA + bsxA = 0

Combine like terms: 2abs + 3abs = 5abs
5abs + absx + absx + -1bsA + bsxA = 0

Combine like terms: absx + absx = 2absx
5abs + 2absx + -1bsA + bsxA = 0

Solving
5abs + 2absx + -1bsA + bsxA = 0

Solving for variable 'a'.

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

Add 'bsA' to each side of the equation.
5abs + 2absx + -1bsA + bsA + bsxA = 0 + bsA

Combine like terms: -1bsA + bsA = 0
5abs + 2absx + 0 + bsxA = 0 + bsA
5abs + 2absx + bsxA = 0 + bsA
Remove the zero:
5abs + 2absx + bsxA = bsA

Add '-1bsxA' to each side of the equation.
5abs + 2absx + bsxA + -1bsxA = bsA + -1bsxA

Combine like terms: bsxA + -1bsxA = 0
5abs + 2absx + 0 = bsA + -1bsxA
5abs + 2absx = bsA + -1bsxA

Reorder the terms:
5abs + 2absx + -1bsA + bsxA = bsA + -1bsA + -1bsxA + bsxA

Combine like terms: bsA + -1bsA = 0
5abs + 2absx + -1bsA + bsxA = 0 + -1bsxA + bsxA
5abs + 2absx + -1bsA + bsxA = -1bsxA + bsxA

Combine like terms: -1bsxA + bsxA = 0
5abs + 2absx + -1bsA + bsxA = 0

Factor out the Greatest Common Factor (GCF), 'bs'.
bs(5a + 2ax + -1A + xA) = 0

Subproblem 1

Set the factor 'bs' equal to zero and attempt to solve: Simplifying bs = 0 Solving bs = 0 Move all terms containing a to the left, all other terms to the right. Add '-1bs' to each side of the equation. bs + -1bs = 0 + -1bs Remove the zero: 0 = -1bs Simplifying 0 = -1bs The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(5a + 2ax + -1A + xA)' equal to zero and attempt to solve: Simplifying 5a + 2ax + -1A + xA = 0 Reorder the terms: -1A + 5a + 2ax + xA = 0 Solving -1A + 5a + 2ax + xA = 0 Move all terms containing a to the left, all other terms to the right. Add 'A' to each side of the equation. -1A + 5a + 2ax + A + xA = 0 + A Reorder the terms: -1A + A + 5a + 2ax + xA = 0 + A Combine like terms: -1A + A = 0 0 + 5a + 2ax + xA = 0 + A 5a + 2ax + xA = 0 + A Remove the zero: 5a + 2ax + xA = A Add '-1xA' to each side of the equation. 5a + 2ax + xA + -1xA = A + -1xA Combine like terms: xA + -1xA = 0 5a + 2ax + 0 = A + -1xA 5a + 2ax = A + -1xA 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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