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

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


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

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

Reorder the terms:
(-2absx + 1a2b2s2 + a2b2s2x) = 3abs(x + 2)
(-2absx + 1a2b2s2 + a2b2s2x) = 3abs(x + 2)

Reorder the terms:
-2absx + 1a2b2s2 + a2b2s2x = 3abs(2 + x)
-2absx + 1a2b2s2 + a2b2s2x = (2 * 3abs + x * 3abs)
-2absx + 1a2b2s2 + a2b2s2x = (6abs + 3absx)

Solving
-2absx + 1a2b2s2 + a2b2s2x = 6abs + 3absx

Solving for variable 'a'.

Reorder the terms:
-6abs + -2absx + -3absx + 1a2b2s2 + a2b2s2x = 6abs + 3absx + -6abs + -3absx

Combine like terms: -2absx + -3absx = -5absx
-6abs + -5absx + 1a2b2s2 + a2b2s2x = 6abs + 3absx + -6abs + -3absx

Reorder the terms:
-6abs + -5absx + 1a2b2s2 + a2b2s2x = 6abs + -6abs + 3absx + -3absx

Combine like terms: 6abs + -6abs = 0
-6abs + -5absx + 1a2b2s2 + a2b2s2x = 0 + 3absx + -3absx
-6abs + -5absx + 1a2b2s2 + a2b2s2x = 3absx + -3absx

Combine like terms: 3absx + -3absx = 0
-6abs + -5absx + 1a2b2s2 + a2b2s2x = 0

Factor out the Greatest Common Factor (GCF), 'abs'.
abs(-6 + -5x + abs + absx) = 0

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 '(-6 + -5x + abs + absx)' equal to zero and attempt to solve: Simplifying -6 + -5x + abs + absx = 0 Reorder the terms: -6 + abs + absx + -5x = 0 Solving -6 + abs + absx + -5x = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + abs + absx + 6 + -5x = 0 + 6 Reorder the terms: -6 + 6 + abs + absx + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + abs + absx + -5x = 0 + 6 abs + absx + -5x = 0 + 6 Combine like terms: 0 + 6 = 6 abs + absx + -5x = 6 Add '5x' to each side of the equation. abs + absx + -5x + 5x = 6 + 5x Combine like terms: -5x + 5x = 0 abs + absx + 0 = 6 + 5x abs + absx = 6 + 5x 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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