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Simplifying abs(4x + -3) = abs(2x + 5) Reorder the terms: abs(-3 + 4x) = abs(2x + 5) (-3 * abs + 4x * abs) = abs(2x + 5) (-3abs + 4absx) = abs(2x + 5) Reorder the terms: -3abs + 4absx = abs(5 + 2x) -3abs + 4absx = (5 * abs + 2x * abs) -3abs + 4absx = (5abs + 2absx) Solving -3abs + 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. -3abs + -5abs + 4absx = 5abs + -5abs + 2absx Combine like terms: -3abs + -5abs = -8abs -8abs + 4absx = 5abs + -5abs + 2absx Combine like terms: 5abs + -5abs = 0 -8abs + 4absx = 0 + 2absx -8abs + 4absx = 2absx Add '-2absx' to each side of the equation. -8abs + 4absx + -2absx = 2absx + -2absx Combine like terms: 4absx + -2absx = 2absx -8abs + 2absx = 2absx + -2absx Combine like terms: 2absx + -2absx = 0 -8abs + 2absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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