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Simplifying abs(4x + 1) = abs(3x + -7) Reorder the terms: abs(1 + 4x) = abs(3x + -7) (1 * abs + 4x * abs) = abs(3x + -7) (1abs + 4absx) = abs(3x + -7) Reorder the terms: 1abs + 4absx = abs(-7 + 3x) 1abs + 4absx = (-7 * abs + 3x * abs) 1abs + 4absx = (-7abs + 3absx) Solving 1abs + 4absx = -7abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7abs' to each side of the equation. 1abs + 7abs + 4absx = -7abs + 7abs + 3absx Combine like terms: 1abs + 7abs = 8abs 8abs + 4absx = -7abs + 7abs + 3absx Combine like terms: -7abs + 7abs = 0 8abs + 4absx = 0 + 3absx 8abs + 4absx = 3absx Add '-3absx' to each side of the equation. 8abs + 4absx + -3absx = 3absx + -3absx Combine like terms: 4absx + -3absx = 1absx 8abs + 1absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 8abs + 1absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(8 + x) = 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 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 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -1x 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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