Solve for X: Complex Fraction Equation with 100/25 and 144/12x Terms

To solve this problem, we'll proceed through the following steps:

• Step 1: Simplify each fraction in the equation.
• Step 2: Combine like terms on both sides.
• Step 3: Solve for $x$.

Let's work through these steps:

Step 1: Simplify each fraction:
$\frac{100}{25} = 4$, $\frac{144}{12} = 12$, $\frac{33}{11} = 3$, $\frac{56}{8} = 7$, $\frac{35}{7} = 5$, $\frac{18}{2} = 9$.

Now our equation becomes:

$4 + 12x - 3 = 7x - 5x + 9$

Step 2: Simplify and combine like terms:
On the left side: $4 - 3 + 12x = 1 + 12x$
On the right side: $7x - 5x + 9 = 2x + 9$

The equation now is:

$1 + 12x = 2x + 9$

Step 3: Solve for $x$:
Subtract $2x$ from both sides:
$1 + 10x = 9$
Subtract $1$ from both sides:
$10x = 8$
Divide both sides by $10$:
$x = \frac{8}{10} = \frac{4}{5}$

Therefore, the solution to the problem is $x = \frac{4}{5}$.