Simplify and Solve: Finding X in 8(x+3) - 1 + 4x = 8(x+3) - 5(x-4)

To solve for $x$ in the equation $8(x+3)-1+4x=8(x+3)-5(x-4)$, follow these steps:

• Step 1: Expand the expressions on both sides of the equation.
  Open up the terms: $8(x + 3)$ becomes $8x + 24$, and $5(x - 4)$ becomes $5x - 20$.

• Step 2: Simplify each side.
  Starting with the left-hand side:
  $8(x + 3) - 1 + 4x$ simplifies to $8x + 24 - 1 + 4x = 12x + 23$.
  For the right-hand side:
  $8(x + 3) - 5(x - 4)$ simplifies to $8x + 24 - 5x + 20 = 3x + 44$.

• Step 3: Set the simplified expressions equal and solve for $x$.
  This gives you the equation: $12x + 23 = 3x + 44$.

• Step 4: Isolate $x$.
  Subtract $3x$ from both sides:
  $12x - 3x + 23 = 44$ simplifies to $9x + 23 = 44$.
  Subtract 23 from both sides to isolate the term with $x$:
  $9x = 21$.

• Step 5: Solve for $x$.
  Divide both sides by 9:
  $x = \frac{21}{9} = \frac{7}{3}$.

Therefore, the solution to the equation is $x = \frac{7}{3}$.