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Simplifying 15 = 3e2x + 9 Reorder the terms: 15 = 9 + 3e2x Solving 15 = 9 + 3e2x Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-3e2x' to each side of the equation. 15 + -3e2x = 9 + 3e2x + -3e2x Combine like terms: 3e2x + -3e2x = 0 15 + -3e2x = 9 + 0 15 + -3e2x = 9 Add '-15' to each side of the equation. 15 + -15 + -3e2x = 9 + -15 Combine like terms: 15 + -15 = 0 0 + -3e2x = 9 + -15 -3e2x = 9 + -15 Combine like terms: 9 + -15 = -6 -3e2x = -6 Divide each side by '-3x'. e2 = 2x-1 Simplifying e2 = 2x-1 Combine like terms: 2x-1 + -2x-1 = 0 e2 + -2x-1 = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -2) = 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 + -2)' equal to zero and attempt to solve: Simplifying e2x + -2 = 0 Reorder the terms: -2 + e2x = 0 Solving -2 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + e2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + e2x = 0 + 2 e2x = 0 + 2 Combine like terms: 0 + 2 = 2 e2x = 2 Divide each side by 'x'. e2 = 2x-1 Simplifying e2 = 2x-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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