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Simplifying abs(2x + -5) = abs(4 + -1x) Reorder the terms: abs(-5 + 2x) = abs(4 + -1x) (-5 * abs + 2x * abs) = abs(4 + -1x) (-5abs + 2absx) = abs(4 + -1x) -5abs + 2absx = (4 * abs + -1x * abs) -5abs + 2absx = (4abs + -1absx) Solving -5abs + 2absx = 4abs + -1absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4abs' to each side of the equation. -5abs + -4abs + 2absx = 4abs + -4abs + -1absx Combine like terms: -5abs + -4abs = -9abs -9abs + 2absx = 4abs + -4abs + -1absx Combine like terms: 4abs + -4abs = 0 -9abs + 2absx = 0 + -1absx -9abs + 2absx = -1absx Add 'absx' to each side of the equation. -9abs + 2absx + absx = -1absx + absx Combine like terms: 2absx + absx = 3absx -9abs + 3absx = -1absx + absx Combine like terms: -1absx + absx = 0 -9abs + 3absx = 0 Factor out the Greatest Common Factor (GCF), '3abs'. 3abs(-3 + x) = 0 Ignore the factor 3.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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