(G-f)(x)=3x-4-5x+1

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Solution for (G-f)(x)=3x-4-5x+1 equation: 


Simplifying
(G + -1f)(x) = 3x + -4 + -5x + 1

Reorder the terms for easier multiplication:
x(G + -1f) = 3x + -4 + -5x + 1
(G * x + -1f * x) = 3x + -4 + -5x + 1

Reorder the terms:
(-1fx + xG) = 3x + -4 + -5x + 1
(-1fx + xG) = 3x + -4 + -5x + 1

Reorder the terms:
-1fx + xG = -4 + 1 + 3x + -5x

Combine like terms: -4 + 1 = -3
-1fx + xG = -3 + 3x + -5x

Combine like terms: 3x + -5x = -2x
-1fx + xG = -3 + -2x

Solving
-1fx + xG = -3 + -2x

Solving for variable 'f'.

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

Add '-1xG' to each side of the equation.
-1fx + xG + -1xG = -3 + -2x + -1xG

Combine like terms: xG + -1xG = 0
-1fx + 0 = -3 + -2x + -1xG
-1fx = -3 + -2x + -1xG

Divide each side by '-1x'.
f = 3x-1 + 2 + G

Simplifying
f = 3x-1 + 2 + G

Reorder the terms:
f = 2 + G + 3x-1

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