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