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

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


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

Reorder the terms:
(-4 + 2x) + 3(x + -1) = 2(x + -1) + -1(x + -3)

Remove parenthesis around (-4 + 2x)
-4 + 2x + 3(x + -1) = 2(x + -1) + -1(x + -3)

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

Reorder the terms:
-4 + -3 + 2x + 3x = 2(x + -1) + -1(x + -3)

Combine like terms: -4 + -3 = -7
-7 + 2x + 3x = 2(x + -1) + -1(x + -3)

Combine like terms: 2x + 3x = 5x
-7 + 5x = 2(x + -1) + -1(x + -3)

Reorder the terms:
-7 + 5x = 2(-1 + x) + -1(x + -3)
-7 + 5x = (-1 * 2 + x * 2) + -1(x + -3)
-7 + 5x = (-2 + 2x) + -1(x + -3)

Reorder the terms:
-7 + 5x = -2 + 2x + -1(-3 + x)
-7 + 5x = -2 + 2x + (-3 * -1 + x * -1)
-7 + 5x = -2 + 2x + (3 + -1x)

Reorder the terms:
-7 + 5x = -2 + 3 + 2x + -1x

Combine like terms: -2 + 3 = 1
-7 + 5x = 1 + 2x + -1x

Combine like terms: 2x + -1x = 1x
-7 + 5x = 1 + 1x

Solving
-7 + 5x = 1 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-7 + 5x + -1x = 1 + 1x + -1x

Combine like terms: 5x + -1x = 4x
-7 + 4x = 1 + 1x + -1x

Combine like terms: 1x + -1x = 0
-7 + 4x = 1 + 0
-7 + 4x = 1

Add '7' to each side of the equation.
-7 + 7 + 4x = 1 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 1 + 7
4x = 1 + 7

Combine like terms: 1 + 7 = 8
4x = 8

Divide each side by '4'.
x = 2

Simplifying
x = 2

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