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Simplifying abs(15x + -5) = abs(35 + -5x) Reorder the terms: abs(-5 + 15x) = abs(35 + -5x) (-5 * abs + 15x * abs) = abs(35 + -5x) (-5abs + 15absx) = abs(35 + -5x) -5abs + 15absx = (35 * abs + -5x * abs) -5abs + 15absx = (35abs + -5absx) Solving -5abs + 15absx = 35abs + -5absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-35abs' to each side of the equation. -5abs + -35abs + 15absx = 35abs + -35abs + -5absx Combine like terms: -5abs + -35abs = -40abs -40abs + 15absx = 35abs + -35abs + -5absx Combine like terms: 35abs + -35abs = 0 -40abs + 15absx = 0 + -5absx -40abs + 15absx = -5absx Add '5absx' to each side of the equation. -40abs + 15absx + 5absx = -5absx + 5absx Combine like terms: 15absx + 5absx = 20absx -40abs + 20absx = -5absx + 5absx Combine like terms: -5absx + 5absx = 0 -40abs + 20absx = 0 Factor out the Greatest Common Factor (GCF), '20abs'. 20abs(-2 + x) = 0 Ignore the factor 20.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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