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Simplifying ABC + BCA + CAB = 111(A + B + C) Combine like terms: ABC + ABC = 2ABC 2ABC + ABC = 111(A + B + C) Combine like terms: 2ABC + ABC = 3ABC 3ABC = 111(A + B + C) 3ABC = (A * 111 + B * 111 + C * 111) 3ABC = (111A + 111B + 111C) Solving 3ABC = 111A + 111B + 111C Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-111A' to each side of the equation. -111A + 3ABC = 111A + 111B + -111A + 111C Reorder the terms: -111A + 3ABC = 111A + -111A + 111B + 111C Combine like terms: 111A + -111A = 0 -111A + 3ABC = 0 + 111B + 111C -111A + 3ABC = 111B + 111C Reorder the terms: -111A + 3ABC + -111B + -111C = 111B + -111B + 111C + -111C Combine like terms: 111B + -111B = 0 -111A + 3ABC + -111B + -111C = 0 + 111C + -111C -111A + 3ABC + -111B + -111C = 111C + -111C Combine like terms: 111C + -111C = 0 -111A + 3ABC + -111B + -111C = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-37A + ABC + -37B + -37C) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-37A + ABC + -37B + -37C)' equal to zero and attempt to solve: Simplifying -37A + ABC + -37B + -37C = 0 Solving -37A + ABC + -37B + -37C = 0 Move all terms containing A to the left, all other terms to the right. Add '37B' to each side of the equation. -37A + ABC + -37B + 37B + -37C = 0 + 37B Combine like terms: -37B + 37B = 0 -37A + ABC + 0 + -37C = 0 + 37B -37A + ABC + -37C = 0 + 37B Remove the zero: -37A + ABC + -37C = 37B Add '37C' to each side of the equation. -37A + ABC + -37C + 37C = 37B + 37C Combine like terms: -37C + 37C = 0 -37A + ABC + 0 = 37B + 37C -37A + ABC = 37B + 37C 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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