Solve for X: Simplifying (6-3(x+4))/5 = (x-3)/2

To solve the equation $\frac{6-3\times(x+4)}{5} = \frac{x-3}{2}$, we follow these steps:

• Step 1: Eliminate Fractions
  Multiply both sides by the least common multiple of the denominators, which is 10: $10 \times \left(\frac{6-3\times(x+4)}{5}\right) = 10 \times \left(\frac{x-3}{2}\right)$
• Step 2: Simplify
  This simplifies to: $2 \times (6 - 3 \times (x+4)) = 5 \times (x - 3)$
• Step 3: Distribute
  Distribute on both sides: $2 \times 6 - 2 \times 3 \times (x+4) = 5x - 15$
• Step 4: Simplify the distribution
  Simplifying gives: $12 - 6 \times (x+4) = 5x - 15$
• Step 5: Further distribute and simplify: $12 - 6x - 24 = 5x - 15$ Combine like terms: $-6x - 12 = 5x - 15$
• Step 6: Solve for $x$
  Add $6x$ to both sides: $-12 = 11x - 15$ Add 15 to both sides: $3 = 11x$ Divide by 11: $x = \frac{3}{11}$

Therefore, the solution to the problem is $x = \frac{3}{11}$.