0.1*(0.5-x)+0.9*(0.5+x)=0.5

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Solution for 0.1*(0.5-x)+0.9*(0.5+x)=0.5 equation: 


Simplifying
0.1(0.5 + -1x) + 0.9(0.5 + x) = 0.5
(0.5 * 0.1 + -1x * 0.1) + 0.9(0.5 + x) = 0.5
(0.05 + -0.1x) + 0.9(0.5 + x) = 0.5
0.05 + -0.1x + (0.5 * 0.9 + x * 0.9) = 0.5
0.05 + -0.1x + (0.45 + 0.9x) = 0.5

Reorder the terms:
0.05 + 0.45 + -0.1x + 0.9x = 0.5

Combine like terms: 0.05 + 0.45 = 0.5
0.5 + -0.1x + 0.9x = 0.5

Combine like terms: -0.1x + 0.9x = 0.8x
0.5 + 0.8x = 0.5

Add '-0.5' to each side of the equation.
0.5 + -0.5 + 0.8x = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.8x = 0.5 + -0.5
0.8x = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.8x = 0.0

Solving
0.8x = 0.0

Solving for variable 'x'.

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

Divide each side by '0.8'.
x = 0

Simplifying
x = 0

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