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Simplifying abs(4x + -19) = abs(8x + 20) Reorder the terms: abs(-19 + 4x) = abs(8x + 20) (-19 * abs + 4x * abs) = abs(8x + 20) (-19abs + 4absx) = abs(8x + 20) Reorder the terms: -19abs + 4absx = abs(20 + 8x) -19abs + 4absx = (20 * abs + 8x * abs) -19abs + 4absx = (20abs + 8absx) Solving -19abs + 4absx = 20abs + 8absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20abs' to each side of the equation. -19abs + -20abs + 4absx = 20abs + -20abs + 8absx Combine like terms: -19abs + -20abs = -39abs -39abs + 4absx = 20abs + -20abs + 8absx Combine like terms: 20abs + -20abs = 0 -39abs + 4absx = 0 + 8absx -39abs + 4absx = 8absx Add '-8absx' to each side of the equation. -39abs + 4absx + -8absx = 8absx + -8absx Combine like terms: 4absx + -8absx = -4absx -39abs + -4absx = 8absx + -8absx Combine like terms: 8absx + -8absx = 0 -39abs + -4absx = 0 Factor out the Greatest Common Factor (GCF), '-1abs'. -1abs(39 + 4x) = 0 Ignore the factor -1.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 '(39 + 4x)' equal to zero and attempt to solve: Simplifying 39 + 4x = 0 Solving 39 + 4x = 0 Move all terms containing a to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 4x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 4x = 0 + -39 4x = 0 + -39 Combine like terms: 0 + -39 = -39 4x = -39 Add '-4x' to each side of the equation. 4x + -4x = -39 + -4x Combine like terms: 4x + -4x = 0 0 = -39 + -4x Simplifying 0 = -39 + -4x 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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