Solve the Equation: -8(2-x) = 1/2 + x

To solve the equation $-8(2-x) = \frac{1}{2} + x$, we will follow these detailed steps:

• Step 1: Distribute the $-8$ to both terms inside the parentheses:
  $-8(2-x) = -8 \times 2 + (-8) \times (-x) = -16 + 8x$.
• Step 2: Rewrite the equation from our distribution:
  $-16 + 8x = \frac{1}{2} + x$.
• Step 3: Move all $x$-terms to one side and constants to the other. Subtract $x$ from both sides:
  $8x - x = \frac{1}{2} + 16$.
• Step 4: Simplify both sides:
  $7x = \frac{1}{2} + 16$.
• Step 5: Combine like terms on the right side:
  Convert $16$ to an equivalent fraction of $\frac{32}{2}$ so we can sum with $\frac{1}{2}$:
  $7x = \frac{1}{2} + \frac{32}{2} = \frac{33}{2}$.
• Step 6: Solve for $x$ by dividing by 7:
  $x = \frac{33}{2} \times \frac{1}{7} = \frac{33}{14}$.

Therefore, the solution to the equation is $x = \frac{33}{14}$.

The choice : $\frac{33}{14}$

matches our solution.