10a+3b+.5c=a+b+c

Solution for 10a+3b+.5c=a+b+c equation:

Simplifying
10a + 3b + 0.5c = a + b + c

Solving
10a + 3b + 0.5c = a + b + c

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
10a + 3b + -1a + 0.5c = a + b + -1a + c

Reorder the terms:
10a + -1a + 3b + 0.5c = a + b + -1a + c

Combine like terms: 10a + -1a = 9a
9a + 3b + 0.5c = a + b + -1a + c

Reorder the terms:
9a + 3b + 0.5c = a + -1a + b + c

Combine like terms: a + -1a = 0
9a + 3b + 0.5c = 0 + b + c
9a + 3b + 0.5c = b + c

Add '-3b' to each side of the equation.
9a + 3b + -3b + 0.5c = b + -3b + c

Combine like terms: 3b + -3b = 0
9a + 0 + 0.5c = b + -3b + c
9a + 0.5c = b + -3b + c

Combine like terms: b + -3b = -2b
9a + 0.5c = -2b + c

Add '-0.5c' to each side of the equation.
9a + 0.5c + -0.5c = -2b + c + -0.5c

Combine like terms: 0.5c + -0.5c = 0.0
9a + 0.0 = -2b + c + -0.5c
9a = -2b + c + -0.5c

Combine like terms: c + -0.5c = 0.5c
9a = -2b + 0.5c

Divide each side by '9'.
a = -0.2222222222b + 0.05555555556c

Simplifying
a = -0.2222222222b + 0.05555555556c