(6-5)+(6-4)+(6-3)+(6-2)+(6-1)+x+(6+1)=7x

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Solution for (6-5)+(6-4)+(6-3)+(6-2)+(6-1)+x+(6+1)=7x equation: 


Simplifying
(6 + -5) + (6 + -4) + (6 + -3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x

Combine like terms: 6 + -5 = 1
(1) + (6 + -4) + (6 + -3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x
1 + (6 + -4) + (6 + -3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x

Combine like terms: 6 + -4 = 2
1 + (2) + (6 + -3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x
1 + 2 + (6 + -3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x

Combine like terms: 6 + -3 = 3
1 + 2 + (3) + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x
1 + 2 + 3 + (6 + -2) + (6 + -1) + x + (6 + 1) = 7x

Combine like terms: 6 + -2 = 4
1 + 2 + 3 + (4) + (6 + -1) + x + (6 + 1) = 7x
1 + 2 + 3 + 4 + (6 + -1) + x + (6 + 1) = 7x

Combine like terms: 6 + -1 = 5
1 + 2 + 3 + 4 + (5) + x + (6 + 1) = 7x
1 + 2 + 3 + 4 + 5 + x + (6 + 1) = 7x

Combine like terms: 6 + 1 = 7
1 + 2 + 3 + 4 + 5 + x + (7) = 7x
1 + 2 + 3 + 4 + 5 + x + 7 = 7x

Reorder the terms:
1 + 2 + 3 + 4 + 5 + 7 + x = 7x

Combine like terms: 1 + 2 = 3
3 + 3 + 4 + 5 + 7 + x = 7x

Combine like terms: 3 + 3 = 6
6 + 4 + 5 + 7 + x = 7x

Combine like terms: 6 + 4 = 10
10 + 5 + 7 + x = 7x

Combine like terms: 10 + 5 = 15
15 + 7 + x = 7x

Combine like terms: 15 + 7 = 22
22 + x = 7x

Solving
22 + x = 7x

Solving for variable 'x'.

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

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

Combine like terms: x + -7x = -6x
22 + -6x = 7x + -7x

Combine like terms: 7x + -7x = 0
22 + -6x = 0

Add '-22' to each side of the equation.
22 + -22 + -6x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -6x = 0 + -22
-6x = 0 + -22

Combine like terms: 0 + -22 = -22
-6x = -22

Divide each side by '-6'.
x = 3.666666667

Simplifying
x = 3.666666667

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