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Simplifying abs(10x + -16) = abs(3x + 19) Reorder the terms: abs(-16 + 10x) = abs(3x + 19) (-16 * abs + 10x * abs) = abs(3x + 19) (-16abs + 10absx) = abs(3x + 19) Reorder the terms: -16abs + 10absx = abs(19 + 3x) -16abs + 10absx = (19 * abs + 3x * abs) -16abs + 10absx = (19abs + 3absx) Solving -16abs + 10absx = 19abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-19abs' to each side of the equation. -16abs + -19abs + 10absx = 19abs + -19abs + 3absx Combine like terms: -16abs + -19abs = -35abs -35abs + 10absx = 19abs + -19abs + 3absx Combine like terms: 19abs + -19abs = 0 -35abs + 10absx = 0 + 3absx -35abs + 10absx = 3absx Add '-3absx' to each side of the equation. -35abs + 10absx + -3absx = 3absx + -3absx Combine like terms: 10absx + -3absx = 7absx -35abs + 7absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 -35abs + 7absx = 0 Factor out the Greatest Common Factor (GCF), '7abs'. 7abs(-5 + x) = 0 Ignore the factor 7.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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