We are asked to solve the equation $2(3x-4)=-5(2x-7)$ for $x$. This involves using the distributive property to expand the terms, combining like terms, and isolating $x$.

1. Problem Description

We are asked to solve the equation $2(3x-4)=-5(2x-7)$ for $x$. This involves using the distributive property to expand the terms, combining like terms, and isolating $x$.

2. Solution Steps

First, we use the distributive property to expand both sides of the equation:

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

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

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

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

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

$16x - 8 = 35$

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

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

$16x = 43$

Finally, we divide both sides of the equation by $16$:

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

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

3. Final Answer

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