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Simplifying abs(8x + -19) = abs(5x + 13) Reorder the terms: abs(-19 + 8x) = abs(5x + 13) (-19 * abs + 8x * abs) = abs(5x + 13) (-19abs + 8absx) = abs(5x + 13) Reorder the terms: -19abs + 8absx = abs(13 + 5x) -19abs + 8absx = (13 * abs + 5x * abs) -19abs + 8absx = (13abs + 5absx) Solving -19abs + 8absx = 13abs + 5absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13abs' to each side of the equation. -19abs + -13abs + 8absx = 13abs + -13abs + 5absx Combine like terms: -19abs + -13abs = -32abs -32abs + 8absx = 13abs + -13abs + 5absx Combine like terms: 13abs + -13abs = 0 -32abs + 8absx = 0 + 5absx -32abs + 8absx = 5absx Add '-5absx' to each side of the equation. -32abs + 8absx + -5absx = 5absx + -5absx Combine like terms: 8absx + -5absx = 3absx -32abs + 3absx = 5absx + -5absx Combine like terms: 5absx + -5absx = 0 -32abs + 3absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-32 + 3x) = 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 '(-32 + 3x)' equal to zero and attempt to solve: Simplifying -32 + 3x = 0 Solving -32 + 3x = 0 Move all terms containing a to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + 3x = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 3x = 0 + 32 3x = 0 + 32 Combine like terms: 0 + 32 = 32 3x = 32 Add '-3x' to each side of the equation. 3x + -3x = 32 + -3x Combine like terms: 3x + -3x = 0 0 = 32 + -3x Simplifying 0 = 32 + -3x 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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