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Simplifying abs(4x + -5) = abs(3x + 12) Reorder the terms: abs(-5 + 4x) = abs(3x + 12) (-5 * abs + 4x * abs) = abs(3x + 12) (-5abs + 4absx) = abs(3x + 12) Reorder the terms: -5abs + 4absx = abs(12 + 3x) -5abs + 4absx = (12 * abs + 3x * abs) -5abs + 4absx = (12abs + 3absx) Solving -5abs + 4absx = 12abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12abs' to each side of the equation. -5abs + -12abs + 4absx = 12abs + -12abs + 3absx Combine like terms: -5abs + -12abs = -17abs -17abs + 4absx = 12abs + -12abs + 3absx Combine like terms: 12abs + -12abs = 0 -17abs + 4absx = 0 + 3absx -17abs + 4absx = 3absx Add '-3absx' to each side of the equation. -17abs + 4absx + -3absx = 3absx + -3absx Combine like terms: 4absx + -3absx = 1absx -17abs + 1absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 -17abs + 1absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-17 + x) = 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 '(-17 + x)' equal to zero and attempt to solve: Simplifying -17 + x = 0 Solving -17 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0 + 17 x = 0 + 17 Combine like terms: 0 + 17 = 17 x = 17 Add '-1x' to each side of the equation. x + -1x = 17 + -1x Combine like terms: x + -1x = 0 0 = 17 + -1x Simplifying 0 = 17 + -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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