(0.1*x)+(0.2*y)+(0.5*z)+(0.2*w)=18

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Solution for (0.1*x)+(0.2*y)+(0.5*z)+(0.2*w)=18 equation: 


Simplifying
(0.1x) + (0.2y) + (0.5z) + (0.2w) = 18

Reorder the terms:
(0.2w) + (0.1x) + (0.2y) + (0.5z) = 18

Solving
(0.2w) + (0.1x) + (0.2y) + (0.5z) = 18

Solving for variable 'w'.

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

Add '(-0.1x)' to each side of the equation.
(0.2w) + (0.1x) + (0.2y) + (-0.1x) + (0.5z) = 18 + (-0.1x)

Reorder the terms:
(0.2w) + (0.1x) + (-0.1x) + (0.2y) + (0.5z) = 18 + (-0.1x)

Combine like terms: (0.1x) + (-0.1x) = 0.0
(0.2w) + 0.0 + (0.2y) + (0.5z) = 18 + (-0.1x)
(0.2w) + (0.2y) + (0.5z) = 18 + (-0.1x)

Add '(-0.2y)' to each side of the equation.
(0.2w) + (0.2y) + (-0.2y) + (0.5z) = 18 + (-0.1x) + (-0.2y)

Combine like terms: (0.2y) + (-0.2y) = 0.0
(0.2w) + 0.0 + (0.5z) = 18 + (-0.1x) + (-0.2y)
(0.2w) + (0.5z) = 18 + (-0.1x) + (-0.2y)

Add '(-0.5z)' to each side of the equation.
(0.2w) + (0.5z) + (-0.5z) = 18 + (-0.1x) + (-0.2y) + (-0.5z)

Combine like terms: (0.5z) + (-0.5z) = 0.0
(0.2w) + 0.0 = 18 + (-0.1x) + (-0.2y) + (-0.5z)
(0.2w) = 18 + (-0.1x) + (-0.2y) + (-0.5z)

Divide each side by '0.2'.
w = 90 + (-0.5x) + (-1y) + (-2.5z)

Simplifying
w = 90 + (-0.5x) + (-1y) + (-2.5z)

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