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Simplifying abs(7x + 12) = abs(x + -8) Reorder the terms: abs(12 + 7x) = abs(x + -8) (12 * abs + 7x * abs) = abs(x + -8) (12abs + 7absx) = abs(x + -8) Reorder the terms: 12abs + 7absx = abs(-8 + x) 12abs + 7absx = (-8 * abs + x * abs) 12abs + 7absx = (-8abs + absx) Solving 12abs + 7absx = -8abs + absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8abs' to each side of the equation. 12abs + 8abs + 7absx = -8abs + 8abs + absx Combine like terms: 12abs + 8abs = 20abs 20abs + 7absx = -8abs + 8abs + absx Combine like terms: -8abs + 8abs = 0 20abs + 7absx = 0 + absx 20abs + 7absx = absx Add '-1absx' to each side of the equation. 20abs + 7absx + -1absx = absx + -1absx Combine like terms: 7absx + -1absx = 6absx 20abs + 6absx = absx + -1absx Combine like terms: absx + -1absx = 0 20abs + 6absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(10 + 3x) = 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 '(10 + 3x)' equal to zero and attempt to solve: Simplifying 10 + 3x = 0 Solving 10 + 3x = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3x = 0 + -10 3x = 0 + -10 Combine like terms: 0 + -10 = -10 3x = -10 Add '-3x' to each side of the equation. 3x + -3x = -10 + -3x Combine like terms: 3x + -3x = 0 0 = -10 + -3x Simplifying 0 = -10 + -3x 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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