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Simplifying abs(2x + -3) = abs(3x + 5) Reorder the terms: abs(-3 + 2x) = abs(3x + 5) (-3 * abs + 2x * abs) = abs(3x + 5) (-3abs + 2absx) = abs(3x + 5) Reorder the terms: -3abs + 2absx = abs(5 + 3x) -3abs + 2absx = (5 * abs + 3x * abs) -3abs + 2absx = (5abs + 3absx) Solving -3abs + 2absx = 5abs + 3absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5abs' to each side of the equation. -3abs + -5abs + 2absx = 5abs + -5abs + 3absx Combine like terms: -3abs + -5abs = -8abs -8abs + 2absx = 5abs + -5abs + 3absx Combine like terms: 5abs + -5abs = 0 -8abs + 2absx = 0 + 3absx -8abs + 2absx = 3absx Add '-3absx' to each side of the equation. -8abs + 2absx + -3absx = 3absx + -3absx Combine like terms: 2absx + -3absx = -1absx -8abs + -1absx = 3absx + -3absx Combine like terms: 3absx + -3absx = 0 -8abs + -1absx = 0 Factor out the Greatest Common Factor (GCF), '-1abs'. -1abs(8 + x) = 0 Ignore the factor -1.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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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