.8k-(k+.5)=.1(k+1)

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Solution for .8k-(k+.5)=.1(k+1) equation: 


Simplifying
0.8k + -1(k + 0.5) = 0.1(k + 1)

Reorder the terms:
0.8k + -1(0.5 + k) = 0.1(k + 1)
0.8k + (0.5 * -1 + k * -1) = 0.1(k + 1)
0.8k + (-0.5 + -1k) = 0.1(k + 1)

Reorder the terms:
-0.5 + 0.8k + -1k = 0.1(k + 1)

Combine like terms: 0.8k + -1k = -0.2k
-0.5 + -0.2k = 0.1(k + 1)

Reorder the terms:
-0.5 + -0.2k = 0.1(1 + k)
-0.5 + -0.2k = (1 * 0.1 + k * 0.1)
-0.5 + -0.2k = (0.1 + 0.1k)

Solving
-0.5 + -0.2k = 0.1 + 0.1k

Solving for variable 'k'.

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

Add '-0.1k' to each side of the equation.
-0.5 + -0.2k + -0.1k = 0.1 + 0.1k + -0.1k

Combine like terms: -0.2k + -0.1k = -0.3k
-0.5 + -0.3k = 0.1 + 0.1k + -0.1k

Combine like terms: 0.1k + -0.1k = 0.0
-0.5 + -0.3k = 0.1 + 0.0
-0.5 + -0.3k = 0.1

Add '0.5' to each side of the equation.
-0.5 + 0.5 + -0.3k = 0.1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.3k = 0.1 + 0.5
-0.3k = 0.1 + 0.5

Combine like terms: 0.1 + 0.5 = 0.6
-0.3k = 0.6

Divide each side by '-0.3'.
k = -2

Simplifying
k = -2

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