(x-1)+2(x-2)+3(x-3)+4(x-4)=100

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Solution for (x-1)+2(x-2)+3(x-3)+4(x-4)=100 equation: 


Simplifying
(x + -1) + 2(x + -2) + 3(x + -3) + 4(x + -4) = 100

Reorder the terms:
(-1 + x) + 2(x + -2) + 3(x + -3) + 4(x + -4) = 100

Remove parenthesis around (-1 + x)
-1 + x + 2(x + -2) + 3(x + -3) + 4(x + -4) = 100

Reorder the terms:
-1 + x + 2(-2 + x) + 3(x + -3) + 4(x + -4) = 100
-1 + x + (-2 * 2 + x * 2) + 3(x + -3) + 4(x + -4) = 100
-1 + x + (-4 + 2x) + 3(x + -3) + 4(x + -4) = 100

Reorder the terms:
-1 + x + -4 + 2x + 3(-3 + x) + 4(x + -4) = 100
-1 + x + -4 + 2x + (-3 * 3 + x * 3) + 4(x + -4) = 100
-1 + x + -4 + 2x + (-9 + 3x) + 4(x + -4) = 100

Reorder the terms:
-1 + x + -4 + 2x + -9 + 3x + 4(-4 + x) = 100
-1 + x + -4 + 2x + -9 + 3x + (-4 * 4 + x * 4) = 100
-1 + x + -4 + 2x + -9 + 3x + (-16 + 4x) = 100

Reorder the terms:
-1 + -4 + -9 + -16 + x + 2x + 3x + 4x = 100

Combine like terms: -1 + -4 = -5
-5 + -9 + -16 + x + 2x + 3x + 4x = 100

Combine like terms: -5 + -9 = -14
-14 + -16 + x + 2x + 3x + 4x = 100

Combine like terms: -14 + -16 = -30
-30 + x + 2x + 3x + 4x = 100

Combine like terms: x + 2x = 3x
-30 + 3x + 3x + 4x = 100

Combine like terms: 3x + 3x = 6x
-30 + 6x + 4x = 100

Combine like terms: 6x + 4x = 10x
-30 + 10x = 100

Solving
-30 + 10x = 100

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + 10x = 100 + 30

Combine like terms: -30 + 30 = 0
0 + 10x = 100 + 30
10x = 100 + 30

Combine like terms: 100 + 30 = 130
10x = 130

Divide each side by '10'.
x = 13

Simplifying
x = 13

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