2(x-1)-3(x-2)=4(x-3)+5(x-4)

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Solution for 2(x-1)-3(x-2)=4(x-3)+5(x-4) equation: 


Simplifying
2(x + -1) + -3(x + -2) = 4(x + -3) + 5(x + -4)

Reorder the terms:
2(-1 + x) + -3(x + -2) = 4(x + -3) + 5(x + -4)
(-1 * 2 + x * 2) + -3(x + -2) = 4(x + -3) + 5(x + -4)
(-2 + 2x) + -3(x + -2) = 4(x + -3) + 5(x + -4)

Reorder the terms:
-2 + 2x + -3(-2 + x) = 4(x + -3) + 5(x + -4)
-2 + 2x + (-2 * -3 + x * -3) = 4(x + -3) + 5(x + -4)
-2 + 2x + (6 + -3x) = 4(x + -3) + 5(x + -4)

Reorder the terms:
-2 + 6 + 2x + -3x = 4(x + -3) + 5(x + -4)

Combine like terms: -2 + 6 = 4
4 + 2x + -3x = 4(x + -3) + 5(x + -4)

Combine like terms: 2x + -3x = -1x
4 + -1x = 4(x + -3) + 5(x + -4)

Reorder the terms:
4 + -1x = 4(-3 + x) + 5(x + -4)
4 + -1x = (-3 * 4 + x * 4) + 5(x + -4)
4 + -1x = (-12 + 4x) + 5(x + -4)

Reorder the terms:
4 + -1x = -12 + 4x + 5(-4 + x)
4 + -1x = -12 + 4x + (-4 * 5 + x * 5)
4 + -1x = -12 + 4x + (-20 + 5x)

Reorder the terms:
4 + -1x = -12 + -20 + 4x + 5x

Combine like terms: -12 + -20 = -32
4 + -1x = -32 + 4x + 5x

Combine like terms: 4x + 5x = 9x
4 + -1x = -32 + 9x

Solving
4 + -1x = -32 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
4 + -1x + -9x = -32 + 9x + -9x

Combine like terms: -1x + -9x = -10x
4 + -10x = -32 + 9x + -9x

Combine like terms: 9x + -9x = 0
4 + -10x = -32 + 0
4 + -10x = -32

Add '-4' to each side of the equation.
4 + -4 + -10x = -32 + -4

Combine like terms: 4 + -4 = 0
0 + -10x = -32 + -4
-10x = -32 + -4

Combine like terms: -32 + -4 = -36
-10x = -36

Divide each side by '-10'.
x = 3.6

Simplifying
x = 3.6

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