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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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