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Simplifying abs(z + 4) = 3abs(z + -4) Reorder the terms: abs(4 + z) = 3abs(z + -4) (4 * abs + z * abs) = 3abs(z + -4) (4abs + absz) = 3abs(z + -4) Reorder the terms: 4abs + absz = 3abs(-4 + z) 4abs + absz = (-4 * 3abs + z * 3abs) 4abs + absz = (-12abs + 3absz) Solving 4abs + absz = -12abs + 3absz Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12abs' to each side of the equation. 4abs + 12abs + absz = -12abs + 12abs + 3absz Combine like terms: 4abs + 12abs = 16abs 16abs + absz = -12abs + 12abs + 3absz Combine like terms: -12abs + 12abs = 0 16abs + absz = 0 + 3absz 16abs + absz = 3absz Add '-3absz' to each side of the equation. 16abs + absz + -3absz = 3absz + -3absz Combine like terms: absz + -3absz = -2absz 16abs + -2absz = 3absz + -3absz Combine like terms: 3absz + -3absz = 0 16abs + -2absz = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(8 + -1z) = 0 Ignore the factor 2.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 '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Add 'z' to each side of the equation. -1z + z = -8 + z Combine like terms: -1z + z = 0 0 = -8 + z Simplifying 0 = -8 + z 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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