abs(3y-2)=abs(19-4y)

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Solution for abs(3y-2)=abs(19-4y) equation:


Simplifying
abs(3y + -2) = abs(19 + -4y)

Reorder the terms:
abs(-2 + 3y) = abs(19 + -4y)
(-2 * abs + 3y * abs) = abs(19 + -4y)
(-2abs + 3absy) = abs(19 + -4y)
-2abs + 3absy = (19 * abs + -4y * abs)
-2abs + 3absy = (19abs + -4absy)

Solving
-2abs + 3absy = 19abs + -4absy

Solving for variable 'a'.

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

Add '-19abs' to each side of the equation.
-2abs + -19abs + 3absy = 19abs + -19abs + -4absy

Combine like terms: -2abs + -19abs = -21abs
-21abs + 3absy = 19abs + -19abs + -4absy

Combine like terms: 19abs + -19abs = 0
-21abs + 3absy = 0 + -4absy
-21abs + 3absy = -4absy

Add '4absy' to each side of the equation.
-21abs + 3absy + 4absy = -4absy + 4absy

Combine like terms: 3absy + 4absy = 7absy
-21abs + 7absy = -4absy + 4absy

Combine like terms: -4absy + 4absy = 0
-21abs + 7absy = 0

Factor out the Greatest Common Factor (GCF), '7abs'.
7abs(-3 + y) = 0

Ignore the factor 7.

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 + y)' equal to zero and attempt to solve: Simplifying -3 + y = 0 Solving -3 + y = 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 + y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + y = 0 + 3 y = 0 + 3 Combine like terms: 0 + 3 = 3 y = 3 Add '-1y' to each side of the equation. y + -1y = 3 + -1y Combine like terms: y + -1y = 0 0 = 3 + -1y Simplifying 0 = 3 + -1y 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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