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

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


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

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

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

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

Solving for variable 'a'.

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

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

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

Combine like terms: -2abs + 2abs = 0
6abs + 3absx = 0 + 4absx
6abs + 3absx = 4absx

Add '-4absx' to each side of the equation.
6abs + 3absx + -4absx = 4absx + -4absx

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

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

Factor out the Greatest Common Factor (GCF), 'abs'.
abs(6 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + x 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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