Let's start by solving each expression:
Expression 1: 1/2 * 20 * (2x + 4) = 200
To find x, we'll divide both sides of the equation by 10, eliminating the 1/2*20 on the left side of the equation.
So, we get: (2x + 4) = 20
Subtract 4 from both sides, we have: 2x = 16
Finally, divide both sides by 2, which gives us the solution: x = 8.
Expression 2: 4 * (x + 5) - x/2 = 48
Let's distribute the 4 to get: 4x + 20 - x/2 = 48
We can convert 'x/2' to '2x/4' for simpler calculation, giving us: 4x + 20 - 2x/4 = 48
Group the x terms, and subtract 20 from both sides:
(4 - 2/4)x = 28
This simplifies to: (15/2)x = 28
Lastly, when we divide both sides by 15/2, we have: x = 8
Expression 3: x + 4/2 + 3x - 2 = 63
Simplify the left side of the equation to get: 4x + 1 = 63
Then, subtract 1 from both sides, which results in: 4x = 62
The final term 'x' is then found by dividing both sides by 4, which gives us: x = 15.5
Expression 4: 8x + 5x = 45
Combine like terms on the left side yield: 13x = 45
Divide by 13 on both sides yields our final solution for this expression: x = 45/13
So, the correct option is C. x = 8, x = 15.5, x = 62/4, x = 45/13.
Answer: C. x = 8, x = 15.5, x = 62/4, x = 45/13.