We are given two linear equations to solve for $x$. The equations are: c) $2(3x-4) = -5(2x-7)$ d) $-4 - 3(5x - 6) = -4(-x - 1) + 6$

1. Problem Description

We are given two linear equations to solve for $x$. The equations are:

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

d) $-4 - 3(5x - 6) = -4(-x - 1) + 6$

2. Solution Steps

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

Step 1: Distribute the constants on both sides of the equation.

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

Step 2: Add $10x$ to both sides.

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

$16x - 8 = 35$

Step 3: Add $8$ to both sides.

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

$16x = 43$

Step 4: Divide both sides by $16$.

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

d) Solve $-4 - 3(5x - 6) = -4(-x - 1) + 6$

Step 1: Distribute the constants on both sides.

$-4 - 15x + 18 = 4x + 4 + 6$

Step 2: Combine like terms on both sides.

$-15x + 14 = 4x + 10$

Step 3: Subtract $4x$ from both sides.

$-15x - 4x + 14 = 4x - 4x + 10$

$-19x + 14 = 10$

Step 4: Subtract $14$ from both sides.

$-19x + 14 - 14 = 10 - 14$

$-19x = -4$

Step 5: Divide both sides by $-19$.

$x = \frac{-4}{-19} = \frac{4}{19}$

3. Final Answer

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

d) $x = \frac{4}{19}$