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Simplifying abs(4x + -5) = abs(x + 9) Reorder the terms: abs(-5 + 4x) = abs(x + 9) (-5 * abs + 4x * abs) = abs(x + 9) (-5abs + 4absx) = abs(x + 9) Reorder the terms: -5abs + 4absx = abs(9 + x) -5abs + 4absx = (9 * abs + x * abs) -5abs + 4absx = (9abs + absx) Solving -5abs + 4absx = 9abs + absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9abs' to each side of the equation. -5abs + -9abs + 4absx = 9abs + -9abs + absx Combine like terms: -5abs + -9abs = -14abs -14abs + 4absx = 9abs + -9abs + absx Combine like terms: 9abs + -9abs = 0 -14abs + 4absx = 0 + absx -14abs + 4absx = absx Add '-1absx' to each side of the equation. -14abs + 4absx + -1absx = absx + -1absx Combine like terms: 4absx + -1absx = 3absx -14abs + 3absx = absx + -1absx Combine like terms: absx + -1absx = 0 -14abs + 3absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-14 + 3x) = 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 '(-14 + 3x)' equal to zero and attempt to solve: Simplifying -14 + 3x = 0 Solving -14 + 3x = 0 Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 3x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3x = 0 + 14 3x = 0 + 14 Combine like terms: 0 + 14 = 14 3x = 14 Add '-3x' to each side of the equation. 3x + -3x = 14 + -3x Combine like terms: 3x + -3x = 0 0 = 14 + -3x Simplifying 0 = 14 + -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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