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Simplifying 2e2x + 6 = 8 Reorder the terms: 6 + 2e2x = 8 Solving 6 + 2e2x = 8 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 2e2x = 8 + -6 Combine like terms: 6 + -6 = 0 0 + 2e2x = 8 + -6 2e2x = 8 + -6 Combine like terms: 8 + -6 = 2 2e2x = 2 Divide each side by '2x'. e2 = x-1 Simplifying e2 = x-1 Combine like terms: x-1 + -1x-1 = 0 e2 + -1x-1 = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -1) = 0Subproblem 1
Set the factor 'x-1' equal to zero and attempt to solve: Simplifying x-1 = 0 Solving x-1 = 0 Move all terms containing e to the left, all other terms to the right. Add '-1x-1' to each side of the equation. x-1 + -1x-1 = 0 + -1x-1 Remove the zero: 0 = -1x-1 Simplifying 0 = -1x-1 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 '(e2x + -1)' equal to zero and attempt to solve: Simplifying e2x + -1 = 0 Reorder the terms: -1 + e2x = 0 Solving -1 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + e2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + e2x = 0 + 1 e2x = 0 + 1 Combine like terms: 0 + 1 = 1 e2x = 1 Divide each side by 'x'. e2 = x-1 Simplifying e2 = x-1 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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