Solve for x: `(x-4)/3 + (2x-3)/35 = (5x-32)/9 - (x+9)/28`

Options

A. 18
B. 19
C. 17
D. 16

Answer

To solve the equation

\[ \frac{x-4}{3} + \frac{2x-3}{35} = \frac{5x-32}{9} - \frac{x+9}{28} \]

we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
First, we need to find the LCM of the denominators on both sides of the equation. The denominators are 3, 35, 9, and 28.

- The LCM of 3 and 35 is \(3 \times 35 = 105\).
- The LCM of 9 and 28 is \(9 \times 28 = 252\).