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Simplifying abs(4x + 9) = abs(2x + -5) Reorder the terms: abs(9 + 4x) = abs(2x + -5) (9 * abs + 4x * abs) = abs(2x + -5) (9abs + 4absx) = abs(2x + -5) Reorder the terms: 9abs + 4absx = abs(-5 + 2x) 9abs + 4absx = (-5 * abs + 2x * abs) 9abs + 4absx = (-5abs + 2absx) Solving 9abs + 4absx = -5abs + 2absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5abs' to each side of the equation. 9abs + 5abs + 4absx = -5abs + 5abs + 2absx Combine like terms: 9abs + 5abs = 14abs 14abs + 4absx = -5abs + 5abs + 2absx Combine like terms: -5abs + 5abs = 0 14abs + 4absx = 0 + 2absx 14abs + 4absx = 2absx Add '-2absx' to each side of the equation. 14abs + 4absx + -2absx = 2absx + -2absx Combine like terms: 4absx + -2absx = 2absx 14abs + 2absx = 2absx + -2absx Combine like terms: 2absx + -2absx = 0 14abs + 2absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(7 + 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 '(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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