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