Solve for X: Finding X in ½(8-x) + ½x = 12-x Linear Equation

To solve the equation $\frac{1}{2} \cdot (8-x) + \frac{1}{2}x = 12 - x$, follow these steps:

• Step 1: Use the distributive property on the left side of the equation.
  • Distribute $\frac{1}{2}$ across $(8-x)$:
  • This gives us $\frac{1}{2} \cdot 8 - \frac{1}{2} \cdot x + \frac{1}{2}x$.
  • Simplify the terms: $4 - \frac{1}{2}x + \frac{1}{2}x$.
• Step 2: Simplify the left side of the equation:
  • The terms $-\frac{1}{2}x$ and $\frac{1}{2}x$ cancel each other out.
  • Thus, the left side simplifies to $4$.
• Step 3: Set the simplified equation equal to the right side:
  • So, we have $4 = 12 - x$.
• Step 4: Solve for $x$ using basic algebra:
  • Add $x$ to both sides to move $x$ to one side: $x + 4 = 12$.
  • Subtract 4 from both sides to solve for $x$: $x = 12 - 4$.
  • This results in $x = 8$.

Therefore, the solution to the equation is $x = 8$.