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Simplifying abs(2x + 4) = abs(5x + -2) Reorder the terms: abs(4 + 2x) = abs(5x + -2) (4 * abs + 2x * abs) = abs(5x + -2) (4abs + 2absx) = abs(5x + -2) Reorder the terms: 4abs + 2absx = abs(-2 + 5x) 4abs + 2absx = (-2 * abs + 5x * abs) 4abs + 2absx = (-2abs + 5absx) Solving 4abs + 2absx = -2abs + 5absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2abs' to each side of the equation. 4abs + 2abs + 2absx = -2abs + 2abs + 5absx Combine like terms: 4abs + 2abs = 6abs 6abs + 2absx = -2abs + 2abs + 5absx Combine like terms: -2abs + 2abs = 0 6abs + 2absx = 0 + 5absx 6abs + 2absx = 5absx Add '-5absx' to each side of the equation. 6abs + 2absx + -5absx = 5absx + -5absx Combine like terms: 2absx + -5absx = -3absx 6abs + -3absx = 5absx + -5absx Combine like terms: 5absx + -5absx = 0 6abs + -3absx = 0 Factor out the Greatest Common Factor (GCF), '3abs'. 3abs(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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