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Simplifying abs(3x + -5) = 2abs(2x + 1) Reorder the terms: abs(-5 + 3x) = 2abs(2x + 1) (-5 * abs + 3x * abs) = 2abs(2x + 1) (-5abs + 3absx) = 2abs(2x + 1) Reorder the terms: -5abs + 3absx = 2abs(1 + 2x) -5abs + 3absx = (1 * 2abs + 2x * 2abs) -5abs + 3absx = (2abs + 4absx) Solving -5abs + 3absx = 2abs + 4absx 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. -5abs + -2abs + 3absx = 2abs + -2abs + 4absx Combine like terms: -5abs + -2abs = -7abs -7abs + 3absx = 2abs + -2abs + 4absx Combine like terms: 2abs + -2abs = 0 -7abs + 3absx = 0 + 4absx -7abs + 3absx = 4absx Add '-4absx' to each side of the equation. -7abs + 3absx + -4absx = 4absx + -4absx Combine like terms: 3absx + -4absx = -1absx -7abs + -1absx = 4absx + -4absx Combine like terms: 4absx + -4absx = 0 -7abs + -1absx = 0 Factor out the Greatest Common Factor (GCF), '-1abs'. -1abs(7 + x) = 0 Ignore the factor -1.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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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