x*0.1+(1-x)*10=x*0.5+(1-x)*5

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Solution for x*0.1+(1-x)*10=x*0.5+(1-x)*5 equation: 


Simplifying
x * 0.1 + (1 + -1x) * 10 = x * 0.5 + (1 + -1x) * 5

Reorder the terms for easier multiplication:
0.1x + (1 + -1x) * 10 = x * 0.5 + (1 + -1x) * 5

Reorder the terms for easier multiplication:
0.1x + 10(1 + -1x) = x * 0.5 + (1 + -1x) * 5
0.1x + (1 * 10 + -1x * 10) = x * 0.5 + (1 + -1x) * 5
0.1x + (10 + -10x) = x * 0.5 + (1 + -1x) * 5

Reorder the terms:
10 + 0.1x + -10x = x * 0.5 + (1 + -1x) * 5

Combine like terms: 0.1x + -10x = -9.9x
10 + -9.9x = x * 0.5 + (1 + -1x) * 5

Reorder the terms for easier multiplication:
10 + -9.9x = 0.5x + (1 + -1x) * 5

Reorder the terms for easier multiplication:
10 + -9.9x = 0.5x + 5(1 + -1x)
10 + -9.9x = 0.5x + (1 * 5 + -1x * 5)
10 + -9.9x = 0.5x + (5 + -5x)

Reorder the terms:
10 + -9.9x = 5 + 0.5x + -5x

Combine like terms: 0.5x + -5x = -4.5x
10 + -9.9x = 5 + -4.5x

Solving
10 + -9.9x = 5 + -4.5x

Solving for variable 'x'.

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

Add '4.5x' to each side of the equation.
10 + -9.9x + 4.5x = 5 + -4.5x + 4.5x

Combine like terms: -9.9x + 4.5x = -5.4x
10 + -5.4x = 5 + -4.5x + 4.5x

Combine like terms: -4.5x + 4.5x = 0.0
10 + -5.4x = 5 + 0.0
10 + -5.4x = 5

Add '-10' to each side of the equation.
10 + -10 + -5.4x = 5 + -10

Combine like terms: 10 + -10 = 0
0 + -5.4x = 5 + -10
-5.4x = 5 + -10

Combine like terms: 5 + -10 = -5
-5.4x = -5

Divide each side by '-5.4'.
x = 0.9259259259

Simplifying
x = 0.9259259259

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