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Simplifying in(-4x + 12) + in(6x) = ln(1 + -1x) Reorder the terms: in(12 + -4x) + in(6x) = ln(1 + -1x) (12 * in + -4x * in) + in(6x) = ln(1 + -1x) (12in + -4inx) + in(6x) = ln(1 + -1x) Remove parenthesis around (6x) 12in + -4inx + in * 6x = ln(1 + -1x) Reorder the terms for easier multiplication: 12in + -4inx + 6in * x = ln(1 + -1x) Multiply in * x 12in + -4inx + 6inx = ln(1 + -1x) Combine like terms: -4inx + 6inx = 2inx 12in + 2inx = ln(1 + -1x) 12in + 2inx = (1 * ln + -1x * ln) 12in + 2inx = (1ln + -1lnx) Solving 12in + 2inx = 1ln + -1lnx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: 12in + 2inx + -1ln + lnx = 1ln + -1ln + -1lnx + lnx Combine like terms: 1ln + -1ln = 0 12in + 2inx + -1ln + lnx = 0 + -1lnx + lnx 12in + 2inx + -1ln + lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 12in + 2inx + -1ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(12i + 2ix + -1l + lx) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing i to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(12i + 2ix + -1l + lx)' equal to zero and attempt to solve: Simplifying 12i + 2ix + -1l + lx = 0 Solving 12i + 2ix + -1l + lx = 0 Move all terms containing i to the left, all other terms to the right. Add 'l' to each side of the equation. 12i + 2ix + -1l + l + lx = 0 + l Combine like terms: -1l + l = 0 12i + 2ix + 0 + lx = 0 + l 12i + 2ix + lx = 0 + l Remove the zero: 12i + 2ix + lx = l Add '-1lx' to each side of the equation. 12i + 2ix + lx + -1lx = l + -1lx Combine like terms: lx + -1lx = 0 12i + 2ix + 0 = l + -1lx 12i + 2ix = l + -1lx 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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