lin(3x+4)=2lin(x+1)

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Solution for lin(3x+4)=2lin(x+1) equation:


Simplifying
lin(3x + 4) = 2lin(x + 1)

Reorder the terms:
iln(4 + 3x) = 2lin(x + 1)
(4 * iln + 3x * iln) = 2lin(x + 1)
(4iln + 3ilnx) = 2lin(x + 1)

Reorder the terms:
4iln + 3ilnx = 2iln(1 + x)
4iln + 3ilnx = (1 * 2iln + x * 2iln)
4iln + 3ilnx = (2iln + 2ilnx)

Solving
4iln + 3ilnx = 2iln + 2ilnx

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-2iln' to each side of the equation.
4iln + -2iln + 3ilnx = 2iln + -2iln + 2ilnx

Combine like terms: 4iln + -2iln = 2iln
2iln + 3ilnx = 2iln + -2iln + 2ilnx

Combine like terms: 2iln + -2iln = 0
2iln + 3ilnx = 0 + 2ilnx
2iln + 3ilnx = 2ilnx

Add '-2ilnx' to each side of the equation.
2iln + 3ilnx + -2ilnx = 2ilnx + -2ilnx

Combine like terms: 3ilnx + -2ilnx = 1ilnx
2iln + 1ilnx = 2ilnx + -2ilnx

Combine like terms: 2ilnx + -2ilnx = 0
2iln + 1ilnx = 0

Factor out the Greatest Common Factor (GCF), 'iln'.
iln(2 + x) = 0

Subproblem 1

Set the factor 'iln' equal to zero and attempt to solve: Simplifying iln = 0 Solving iln = 0 Move all terms containing i to the left, all other terms to the right. Simplifying iln = 0 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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