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Simplifying abs(7 + -3x) = abs(2x + -8) (7 * abs + -3x * abs) = abs(2x + -8) (7abs + -3absx) = abs(2x + -8) Reorder the terms: 7abs + -3absx = abs(-8 + 2x) 7abs + -3absx = (-8 * abs + 2x * abs) 7abs + -3absx = (-8abs + 2absx) Solving 7abs + -3absx = -8abs + 2absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8abs' to each side of the equation. 7abs + 8abs + -3absx = -8abs + 8abs + 2absx Combine like terms: 7abs + 8abs = 15abs 15abs + -3absx = -8abs + 8abs + 2absx Combine like terms: -8abs + 8abs = 0 15abs + -3absx = 0 + 2absx 15abs + -3absx = 2absx Add '-2absx' to each side of the equation. 15abs + -3absx + -2absx = 2absx + -2absx Combine like terms: -3absx + -2absx = -5absx 15abs + -5absx = 2absx + -2absx Combine like terms: 2absx + -2absx = 0 15abs + -5absx = 0 Factor out the Greatest Common Factor (GCF), '5abs'. 5abs(3 + -1x) = 0 Ignore the factor 5.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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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