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Simplifying abs(2x + -16) = abs(7x + 9) Reorder the terms: abs(-16 + 2x) = abs(7x + 9) (-16 * abs + 2x * abs) = abs(7x + 9) (-16abs + 2absx) = abs(7x + 9) Reorder the terms: -16abs + 2absx = abs(9 + 7x) -16abs + 2absx = (9 * abs + 7x * abs) -16abs + 2absx = (9abs + 7absx) Solving -16abs + 2absx = 9abs + 7absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9abs' to each side of the equation. -16abs + -9abs + 2absx = 9abs + -9abs + 7absx Combine like terms: -16abs + -9abs = -25abs -25abs + 2absx = 9abs + -9abs + 7absx Combine like terms: 9abs + -9abs = 0 -25abs + 2absx = 0 + 7absx -25abs + 2absx = 7absx Add '-7absx' to each side of the equation. -25abs + 2absx + -7absx = 7absx + -7absx Combine like terms: 2absx + -7absx = -5absx -25abs + -5absx = 7absx + -7absx Combine like terms: 7absx + -7absx = 0 -25abs + -5absx = 0 Factor out the Greatest Common Factor (GCF), '-5abs'. -5abs(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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