.45x+.05(20-x)=.10(50)

Solution for .45x+.05(20-x)=.10(50) equation:

Simplifying
0.45x + 0.05(20 + -1x) = 0.10(50)
0.45x + (20 * 0.05 + -1x * 0.05) = 0.10(50)
0.45x + (1 + -0.05x) = 0.10(50)

Reorder the terms:
1 + 0.45x + -0.05x = 0.10(50)

Combine like terms: 0.45x + -0.05x = 0.4x
1 + 0.4x = 0.10(50)

Multiply 0.10 * 50
1 + 0.4x = 5

Solving
1 + 0.4x = 5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + 0.4x = 5 + -1

Combine like terms: 1 + -1 = 0
0 + 0.4x = 5 + -1
0.4x = 5 + -1

Combine like terms: 5 + -1 = 4
0.4x = 4

Divide each side by '0.4'.
x = 10

Simplifying
x = 10