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Simplifying abs(8x + -12) = abs(3x + 7) Reorder the terms: abs(-12 + 8x) = abs(3x + 7) (-12 * abs + 8x * abs) = abs(3x + 7) (-12abs + 8absx) = abs(3x + 7) Reorder the terms: -12abs + 8absx = abs(7 + 3x) -12abs + 8absx = (7 * abs + 3x * abs) -12abs + 8absx = (7abs + 3absx) Solving -12abs + 8absx = 7abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7abs' to each side of the equation. -12abs + -7abs + 8absx = 7abs + -7abs + 3absx Combine like terms: -12abs + -7abs = -19abs -19abs + 8absx = 7abs + -7abs + 3absx Combine like terms: 7abs + -7abs = 0 -19abs + 8absx = 0 + 3absx -19abs + 8absx = 3absx Add '-3absx' to each side of the equation. -19abs + 8absx + -3absx = 3absx + -3absx Combine like terms: 8absx + -3absx = 5absx -19abs + 5absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 -19abs + 5absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-19 + 5x) = 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 '(-19 + 5x)' equal to zero and attempt to solve: Simplifying -19 + 5x = 0 Solving -19 + 5x = 0 Move all terms containing a to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 5x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 5x = 0 + 19 5x = 0 + 19 Combine like terms: 0 + 19 = 19 5x = 19 Add '-5x' to each side of the equation. 5x + -5x = 19 + -5x Combine like terms: 5x + -5x = 0 0 = 19 + -5x Simplifying 0 = 19 + -5x 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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