We are asked to solve the linear equation $7(2x-4) + 3(5-3x) = 2$ for $x$.

1. Problem Description

We are asked to solve the linear equation $7(2x-4) + 3(5-3x) = 2$ for $x$.

2. Solution Steps

First, expand the terms in the equation:

$7(2x-4) + 3(5-3x) = 2$

$14x - 28 + 15 - 9x = 2$

Combine like terms on the left side:

$(14x - 9x) + (-28 + 15) = 2$

$5x - 13 = 2$

Add 13 to both sides of the equation:

$5x - 13 + 13 = 2 + 13$

$5x = 15$

Divide both sides by 5:

$\frac{5x}{5} = \frac{15}{5}$

$x = 3$

3. Final Answer

The solution is $x = 3$.