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Simplifying abs(2x + 1) = abs(4x + -5) Reorder the terms: abs(1 + 2x) = abs(4x + -5) (1 * abs + 2x * abs) = abs(4x + -5) (1abs + 2absx) = abs(4x + -5) Reorder the terms: 1abs + 2absx = abs(-5 + 4x) 1abs + 2absx = (-5 * abs + 4x * abs) 1abs + 2absx = (-5abs + 4absx) Solving 1abs + 2absx = -5abs + 4absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5abs' to each side of the equation. 1abs + 5abs + 2absx = -5abs + 5abs + 4absx Combine like terms: 1abs + 5abs = 6abs 6abs + 2absx = -5abs + 5abs + 4absx Combine like terms: -5abs + 5abs = 0 6abs + 2absx = 0 + 4absx 6abs + 2absx = 4absx Add '-4absx' to each side of the equation. 6abs + 2absx + -4absx = 4absx + -4absx Combine like terms: 2absx + -4absx = -2absx 6abs + -2absx = 4absx + -4absx Combine like terms: 4absx + -4absx = 0 6abs + -2absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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