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