Solve the equation $\frac{3-5x}{7} - \frac{x}{4} = 2 + \frac{5-4x}{8}$ for $x$.

1. Problem Description

Solve the equation $\frac{3-5x}{7} - \frac{x}{4} = 2 + \frac{5-4x}{8}$ for $x$.

2. Solution Steps

First, multiply both sides of the equation by the least common multiple (LCM) of the denominators 7, 4, and 8, which is

5

6. $56 \cdot (\frac{3-5x}{7} - \frac{x}{4}) = 56 \cdot (2 + \frac{5-4x}{8})$

$56 \cdot \frac{3-5x}{7} - 56 \cdot \frac{x}{4} = 56 \cdot 2 + 56 \cdot \frac{5-4x}{8}$

$8(3-5x) - 14x = 112 + 7(5-4x)$

Expand the terms.

$24 - 40x - 14x = 112 + 35 - 28x$

$24 - 54x = 147 - 28x$

Add $54x$ to both sides.

$24 = 147 - 28x + 54x$

$24 = 147 + 26x$

Subtract 147 from both sides.

$24 - 147 = 26x$

$-123 = 26x$

Divide both sides by

2

6. $x = \frac{-123}{26}$

3. Final Answer

$x = -\frac{123}{26}$