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Simplifying abs(8x + 14) = abs(3x + -3) Reorder the terms: abs(14 + 8x) = abs(3x + -3) (14 * abs + 8x * abs) = abs(3x + -3) (14abs + 8absx) = abs(3x + -3) Reorder the terms: 14abs + 8absx = abs(-3 + 3x) 14abs + 8absx = (-3 * abs + 3x * abs) 14abs + 8absx = (-3abs + 3absx) Solving 14abs + 8absx = -3abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3abs' to each side of the equation. 14abs + 3abs + 8absx = -3abs + 3abs + 3absx Combine like terms: 14abs + 3abs = 17abs 17abs + 8absx = -3abs + 3abs + 3absx Combine like terms: -3abs + 3abs = 0 17abs + 8absx = 0 + 3absx 17abs + 8absx = 3absx Add '-3absx' to each side of the equation. 17abs + 8absx + -3absx = 3absx + -3absx Combine like terms: 8absx + -3absx = 5absx 17abs + 5absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 17abs + 5absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(17 + 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 '(17 + 5x)' equal to zero and attempt to solve: Simplifying 17 + 5x = 0 Solving 17 + 5x = 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 + 5x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 5x = 0 + -17 5x = 0 + -17 Combine like terms: 0 + -17 = -17 5x = -17 Add '-5x' to each side of the equation. 5x + -5x = -17 + -5x Combine like terms: 5x + -5x = 0 0 = -17 + -5x Simplifying 0 = -17 + -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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