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