The problem asks us to solve the following equations: a) $5x - 3 = -17$ b) $7x + 6 = -2x - 48$ c) $5x - 8 = 7x - 1$ d) $6(x - 2) = -3(x - 1) + 2$

1. Problem Description

The problem asks us to solve the following equations:

a) $5x - 3 = -17$

b) $7x + 6 = -2x - 48$

c) $5x - 8 = 7x - 1$

d) $6(x - 2) = -3(x - 1) + 2$

2. Solution Steps

a) $5x - 3 = -17$

Add 3 to both sides:

$5x - 3 + 3 = -17 + 3$

$5x = -14$

Divide both sides by 5:

$x = \frac{-14}{5}$

b) $7x + 6 = -2x - 48$

Add $2x$ to both sides:

$7x + 2x + 6 = -2x + 2x - 48$

$9x + 6 = -48$

Subtract 6 from both sides:

$9x + 6 - 6 = -48 - 6$

$9x = -54$

Divide both sides by 9:

$x = \frac{-54}{9}$

$x = -6$

c) $5x - 8 = 7x - 1$

Subtract $5x$ from both sides:

$5x - 5x - 8 = 7x - 5x - 1$

$-8 = 2x - 1$

Add 1 to both sides:

$-8 + 1 = 2x - 1 + 1$

$-7 = 2x$

Divide both sides by 2:

$x = \frac{-7}{2}$

d) $6(x - 2) = -3(x - 1) + 2$

Expand both sides:

$6x - 12 = -3x + 3 + 2$

$6x - 12 = -3x + 5$

Add $3x$ to both sides:

$6x + 3x - 12 = -3x + 3x + 5$

$9x - 12 = 5$

Add 12 to both sides:

$9x - 12 + 12 = 5 + 12$

$9x = 17$

Divide both sides by 9:

$x = \frac{17}{9}$

3. Final Answer

a) $x = -\frac{14}{5}$

b) $x = -6$

c) $x = -\frac{7}{2}$

d) $x = \frac{17}{9}$