The problem is to solve the equation $2(3x - 4) = -5(2x - 7)$ for $x$.

1. Problem Description

The problem is to solve the equation $2(3x - 4) = -5(2x - 7)$ for $x$.

2. Solution Steps

First, distribute the constants on both sides of the equation:

$2(3x - 4) = 6x - 8$

$-5(2x - 7) = -10x + 35$

So, the equation becomes:

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

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 of the equation by 16:

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

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

3. Final Answer

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