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Simplifying 4times(2c + 8) = 5time(c + 4) Reorder the terms: 4eimst(8 + 2c) = 5time(c + 4) (8 * 4eimst + 2c * 4eimst) = 5time(c + 4) Reorder the terms: (8ceimst + 32eimst) = 5time(c + 4) (8ceimst + 32eimst) = 5time(c + 4) Reorder the terms: 8ceimst + 32eimst = 5eimt(4 + c) 8ceimst + 32eimst = (4 * 5eimt + c * 5eimt) Reorder the terms: 8ceimst + 32eimst = (5ceimt + 20eimt) 8ceimst + 32eimst = (5ceimt + 20eimt) Solving 8ceimst + 32eimst = 5ceimt + 20eimt Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5ceimt' to each side of the equation. 8ceimst + -5ceimt + 32eimst = 5ceimt + -5ceimt + 20eimt Combine like terms: 5ceimt + -5ceimt = 0 8ceimst + -5ceimt + 32eimst = 0 + 20eimt 8ceimst + -5ceimt + 32eimst = 20eimt Add '-32eimst' to each side of the equation. 8ceimst + -5ceimt + 32eimst + -32eimst = -32eimst + 20eimt Combine like terms: 32eimst + -32eimst = 0 8ceimst + -5ceimt + 0 = -32eimst + 20eimt 8ceimst + -5ceimt = -32eimst + 20eimt Reorder the terms: 8ceimst + -5ceimt + 32eimst + -20eimt = -32eimst + 32eimst + 20eimt + -20eimt Combine like terms: -32eimst + 32eimst = 0 8ceimst + -5ceimt + 32eimst + -20eimt = 0 + 20eimt + -20eimt 8ceimst + -5ceimt + 32eimst + -20eimt = 20eimt + -20eimt Combine like terms: 20eimt + -20eimt = 0 8ceimst + -5ceimt + 32eimst + -20eimt = 0 Factor out the Greatest Common Factor (GCF), 'eimt'. eimt(8cs + -5c + 32s + -20) = 0Subproblem 1
Set the factor 'eimt' equal to zero and attempt to solve: Simplifying eimt = 0 Solving eimt = 0 Move all terms containing c to the left, all other terms to the right. Add '-1eimt' to each side of the equation. eimt + -1eimt = 0 + -1eimt Remove the zero: 0 = -1eimt Simplifying 0 = -1eimt 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 '(8cs + -5c + 32s + -20)' equal to zero and attempt to solve: Simplifying 8cs + -5c + 32s + -20 = 0 Reorder the terms: -20 + -5c + 8cs + 32s = 0 Solving -20 + -5c + 8cs + 32s = 0 Move all terms containing c to the left, all other terms to the right. Add '20' to each side of the equation. -20 + -5c + 8cs + 20 + 32s = 0 + 20 Reorder the terms: -20 + 20 + -5c + 8cs + 32s = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -5c + 8cs + 32s = 0 + 20 -5c + 8cs + 32s = 0 + 20 Combine like terms: 0 + 20 = 20 -5c + 8cs + 32s = 20 Add '-32s' to each side of the equation. -5c + 8cs + 32s + -32s = 20 + -32s Combine like terms: 32s + -32s = 0 -5c + 8cs + 0 = 20 + -32s -5c + 8cs = 20 + -32s 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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