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Simplifying abs(2x + 54) = abs(x + 11) Reorder the terms: abs(54 + 2x) = abs(x + 11) (54 * abs + 2x * abs) = abs(x + 11) (54abs + 2absx) = abs(x + 11) Reorder the terms: 54abs + 2absx = abs(11 + x) 54abs + 2absx = (11 * abs + x * abs) 54abs + 2absx = (11abs + absx) Solving 54abs + 2absx = 11abs + absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11abs' to each side of the equation. 54abs + -11abs + 2absx = 11abs + -11abs + absx Combine like terms: 54abs + -11abs = 43abs 43abs + 2absx = 11abs + -11abs + absx Combine like terms: 11abs + -11abs = 0 43abs + 2absx = 0 + absx 43abs + 2absx = absx Add '-1absx' to each side of the equation. 43abs + 2absx + -1absx = absx + -1absx Combine like terms: 2absx + -1absx = 1absx 43abs + 1absx = absx + -1absx Combine like terms: absx + -1absx = 0 43abs + 1absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(43 + 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 '(43 + x)' equal to zero and attempt to solve: Simplifying 43 + x = 0 Solving 43 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + x = 0 + -43 Combine like terms: 43 + -43 = 0 0 + x = 0 + -43 x = 0 + -43 Combine like terms: 0 + -43 = -43 x = -43 Add '-1x' to each side of the equation. x + -1x = -43 + -1x Combine like terms: x + -1x = 0 0 = -43 + -1x Simplifying 0 = -43 + -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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