abs(3x-2)=abs(4-x)

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


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

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

Solving
-2abs + 3absx = 4abs + -1absx

Solving for variable 'a'.

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

Add '-4abs' to each side of the equation.
-2abs + -4abs + 3absx = 4abs + -4abs + -1absx

Combine like terms: -2abs + -4abs = -6abs
-6abs + 3absx = 4abs + -4abs + -1absx

Combine like terms: 4abs + -4abs = 0
-6abs + 3absx = 0 + -1absx
-6abs + 3absx = -1absx

Add 'absx' to each side of the equation.
-6abs + 3absx + absx = -1absx + absx

Combine like terms: 3absx + absx = 4absx
-6abs + 4absx = -1absx + absx

Combine like terms: -1absx + absx = 0
-6abs + 4absx = 0

Factor out the Greatest Common Factor (GCF), '2abs'.
2abs(-3 + 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -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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