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

1. Problem Description

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

2. Solution Steps

First, distribute the $2$ on the left side and the $-5$ on the right side:

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

$6x - 8 = -10x + 35$

Next, add $10x$ to both sides of the equation:

$6x - 8 + 10x = -10x + 35 + 10x$

$16x - 8 = 35$

Then, add $8$ to both sides of the equation:

$16x - 8 + 8 = 35 + 8$

$16x = 43$

Finally, divide both sides by $16$:

$\frac{16x}{16} = \frac{43}{16}$

$x = \frac{43}{16}$

3. Final Answer

$x = \frac{43}{16}$