Solve for X: Finding X in (1/4)(x-16) + (3/4)x = 8x-11

To solve this problem, we'll eliminate fractions by multiplying the entire equation by the least common denominator, and then proceed with algebraic manipulation:

• Step 1: Multiply every term by the least common denominator, $4$, to eliminate fractions:
  $4 \times \left(\frac{1}{4}(x - 16) + \frac{3}{4}x\right) = 4 \times (8x - 11)$.

• Step 2: This simplifies to: $1(x - 16) + 3x = 32x - 44$.

• Step 3: Distribute within the brackets:
  $x - 16 + 3x = 32x - 44$.

• Step 4: Combine like terms on the left-hand side:
  $4x - 16 = 32x - 44$.

• Step 5: To isolate terms containing $x$, subtract $4x$ from both sides:
  $-16 = 28x - 44$.

• Step 6: Add 44 to both sides to further isolate $x$:
  $28 = 28x$.

• Step 7: Divide both sides by 28 to solve for $x$:
  $x = 1$.

Therefore, the solution to the problem is $x = 1$.