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Simplifying abs(4x + 2) = abs(2x + 5) Reorder the terms: abs(2 + 4x) = abs(2x + 5) (2 * abs + 4x * abs) = abs(2x + 5) (2abs + 4absx) = abs(2x + 5) Reorder the terms: 2abs + 4absx = abs(5 + 2x) 2abs + 4absx = (5 * abs + 2x * abs) 2abs + 4absx = (5abs + 2absx) Solving 2abs + 4absx = 5abs + 2absx 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. 2abs + -5abs + 4absx = 5abs + -5abs + 2absx Combine like terms: 2abs + -5abs = -3abs -3abs + 4absx = 5abs + -5abs + 2absx Combine like terms: 5abs + -5abs = 0 -3abs + 4absx = 0 + 2absx -3abs + 4absx = 2absx Add '-2absx' to each side of the equation. -3abs + 4absx + -2absx = 2absx + -2absx Combine like terms: 4absx + -2absx = 2absx -3abs + 2absx = 2absx + -2absx Combine like terms: 2absx + -2absx = 0 -3abs + 2absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -2x 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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