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Simplifying abs(z + -1) = 2abs(z + 1) Reorder the terms: abs(-1 + z) = 2abs(z + 1) (-1 * abs + z * abs) = 2abs(z + 1) (-1abs + absz) = 2abs(z + 1) Reorder the terms: -1abs + absz = 2abs(1 + z) -1abs + absz = (1 * 2abs + z * 2abs) -1abs + absz = (2abs + 2absz) Solving -1abs + absz = 2abs + 2absz 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. -1abs + -2abs + absz = 2abs + -2abs + 2absz Combine like terms: -1abs + -2abs = -3abs -3abs + absz = 2abs + -2abs + 2absz Combine like terms: 2abs + -2abs = 0 -3abs + absz = 0 + 2absz -3abs + absz = 2absz Add '-2absz' to each side of the equation. -3abs + absz + -2absz = 2absz + -2absz Combine like terms: absz + -2absz = -1absz -3abs + -1absz = 2absz + -2absz Combine like terms: 2absz + -2absz = 0 -3abs + -1absz = 0 Factor out the Greatest Common Factor (GCF), '-1abs'. -1abs(3 + z) = 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 '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 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 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Add '-1z' to each side of the equation. z + -1z = -3 + -1z Combine like terms: z + -1z = 0 0 = -3 + -1z Simplifying 0 = -3 + -1z 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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