0.5k(11-k)+(6-k+1)=0.5(k+1)(11-k+1)

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Solution for 0.5k(11-k)+(6-k+1)=0.5(k+1)(11-k+1) equation: 


Simplifying
0.5k(11 + -1k) + (6 + -1k + 1) = 0.5(k + 1)(11 + -1k + 1)
(11 * 0.5k + -1k * 0.5k) + (6 + -1k + 1) = 0.5(k + 1)(11 + -1k + 1)
(5.5k + -0.5k2) + (6 + -1k + 1) = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
5.5k + -0.5k2 + (6 + 1 + -1k) = 0.5(k + 1)(11 + -1k + 1)

Combine like terms: 6 + 1 = 7
5.5k + -0.5k2 + (7 + -1k) = 0.5(k + 1)(11 + -1k + 1)

Remove parenthesis around (7 + -1k)
5.5k + -0.5k2 + 7 + -1k = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
7 + 5.5k + -1k + -0.5k2 = 0.5(k + 1)(11 + -1k + 1)

Combine like terms: 5.5k + -1k = 4.5k
7 + 4.5k + -0.5k2 = 0.5(k + 1)(11 + -1k + 1)

Reorder the terms:
7 + 4.5k + -0.5k2 = 0.5(1 + k)(11 + -1k + 1)

Reorder the terms:
7 + 4.5k + -0.5k2 = 0.5(1 + k)(11 + 1 + -1k)

Combine like terms: 11 + 1 = 12
7 + 4.5k + -0.5k2 = 0.5(1 + k)(12 + -1k)

Multiply (1 + k) * (12 + -1k)
7 + 4.5k + -0.5k2 = 0.5(1(12 + -1k) + k(12 + -1k))
7 + 4.5k + -0.5k2 = 0.5((12 * 1 + -1k * 1) + k(12 + -1k))
7 + 4.5k + -0.5k2 = 0.5((12 + -1k) + k(12 + -1k))
7 + 4.5k + -0.5k2 = 0.5(12 + -1k + (12 * k + -1k * k))
7 + 4.5k + -0.5k2 = 0.5(12 + -1k + (12k + -1k2))

Combine like terms: -1k + 12k = 11k
7 + 4.5k + -0.5k2 = 0.5(12 + 11k + -1k2)
7 + 4.5k + -0.5k2 = (12 * 0.5 + 11k * 0.5 + -1k2 * 0.5)
7 + 4.5k + -0.5k2 = (6 + 5.5k + -0.5k2)

Add '0.5k2' to each side of the equation.
7 + 4.5k + -0.5k2 + 0.5k2 = 6 + 5.5k + -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
7 + 4.5k + 0.0 = 6 + 5.5k + -0.5k2 + 0.5k2
7 + 4.5k = 6 + 5.5k + -0.5k2 + 0.5k2

Combine like terms: -0.5k2 + 0.5k2 = 0.0
7 + 4.5k = 6 + 5.5k + 0.0
7 + 4.5k = 6 + 5.5k

Solving
7 + 4.5k = 6 + 5.5k

Solving for variable 'k'.

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

Add '-5.5k' to each side of the equation.
7 + 4.5k + -5.5k = 6 + 5.5k + -5.5k

Combine like terms: 4.5k + -5.5k = -1k
7 + -1k = 6 + 5.5k + -5.5k

Combine like terms: 5.5k + -5.5k = 0.0
7 + -1k = 6 + 0.0
7 + -1k = 6

Add '-7' to each side of the equation.
7 + -7 + -1k = 6 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 6 + -7
-1k = 6 + -7

Combine like terms: 6 + -7 = -1
-1k = -1

Divide each side by '-1'.
k = 1

Simplifying
k = 1

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