abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4)=0

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Solution for abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4)=0 equation:


Simplifying
abs(x + -1) + abs(x + -2) + abs(x + -3) + abs(x + -4) = 0

Reorder the terms:
abs(-1 + x) + abs(x + -2) + abs(x + -3) + abs(x + -4) = 0
(-1 * abs + x * abs) + abs(x + -2) + abs(x + -3) + abs(x + -4) = 0
(-1abs + absx) + abs(x + -2) + abs(x + -3) + abs(x + -4) = 0

Reorder the terms:
-1abs + absx + abs(-2 + x) + abs(x + -3) + abs(x + -4) = 0
-1abs + absx + (-2 * abs + x * abs) + abs(x + -3) + abs(x + -4) = 0
-1abs + absx + (-2abs + absx) + abs(x + -3) + abs(x + -4) = 0

Reorder the terms:
-1abs + absx + -2abs + absx + abs(-3 + x) + abs(x + -4) = 0
-1abs + absx + -2abs + absx + (-3 * abs + x * abs) + abs(x + -4) = 0
-1abs + absx + -2abs + absx + (-3abs + absx) + abs(x + -4) = 0

Reorder the terms:
-1abs + absx + -2abs + absx + -3abs + absx + abs(-4 + x) = 0
-1abs + absx + -2abs + absx + -3abs + absx + (-4 * abs + x * abs) = 0
-1abs + absx + -2abs + absx + -3abs + absx + (-4abs + absx) = 0

Reorder the terms:
-1abs + -2abs + -3abs + -4abs + absx + absx + absx + absx = 0

Combine like terms: -1abs + -2abs = -3abs
-3abs + -3abs + -4abs + absx + absx + absx + absx = 0

Combine like terms: -3abs + -3abs = -6abs
-6abs + -4abs + absx + absx + absx + absx = 0

Combine like terms: -6abs + -4abs = -10abs
-10abs + absx + absx + absx + absx = 0

Combine like terms: absx + absx = 2absx
-10abs + 2absx + absx + absx = 0

Combine like terms: 2absx + absx = 3absx
-10abs + 3absx + absx = 0

Combine like terms: 3absx + absx = 4absx
-10abs + 4absx = 0

Solving
-10abs + 4absx = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '2abs'.
2abs(-5 + 2x) = 0

Ignore the factor 2.

Subproblem 1

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