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