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Simplifying abs(2x) = abs(5 + -2x) Remove parenthesis around (2x) abs * 2x = abs(5 + -2x) Reorder the terms for easier multiplication: 2abs * x = abs(5 + -2x) Multiply abs * x 2absx = abs(5 + -2x) 2absx = (5 * abs + -2x * abs) 2absx = (5abs + -2absx) Solving 2absx = 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. -5abs + 2absx = 5abs + -5abs + -2absx Combine like terms: 5abs + -5abs = 0 -5abs + 2absx = 0 + -2absx -5abs + 2absx = -2absx Add '2absx' to each side of the equation. -5abs + 2absx + 2absx = -2absx + 2absx Combine like terms: 2absx + 2absx = 4absx -5abs + 4absx = -2absx + 2absx Combine like terms: -2absx + 2absx = 0 -5abs + 4absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-5 + 4x) = 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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 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 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Add '-4x' to each side of the equation. 4x + -4x = 5 + -4x Combine like terms: 4x + -4x = 0 0 = 5 + -4x Simplifying 0 = 5 + -4x 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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