Let's analyze and solve the given equations in the uploaded image.

Problem 1:

Equation:
$5(x - 6) = 55$

Step-by-step Solution:

1. Expand the left-hand side:
   $5x - 30 = 55$
2. Add 30 to both sides:
   $5x = 85$
3. Divide by 5:
   $x = 17$

Solution:

$x = 17$

Problem 2:

Equation:
$-8(x - 8) = -40$

Step-by-step Solution:

1. Expand the left-hand side:
   $-8x + 64 = -40$
2. Subtract 64 from both sides:
   $-8x = -104$
3. Divide by -8:
   $x = 13$

Solution:

$x = 13$

Problem 3:

Equation:
$-9 + \frac{e}{7} + 13 = -2 + 20$

Step-by-step Solution:

1. Simplify constants on each side:
   Left-hand side: $-9 + 13 + \frac{e}{7} = 4 + \frac{e}{7}$
   Right-hand side: $-2 + 20 = 18$
   The equation becomes:
   $4 + \frac{e}{7} = 18$

2. Subtract 4 from both sides:
   $\frac{e}{7} = 14$

3. Multiply through by 7:
   $e = 98$

Solution:

$e = 98$

Would you like further explanations, or do you have specific questions?

Related Questions:

1. What happens if you check your solutions for each equation?
2. How can you simplify multi-step equations to single-variable ones?
3. Why is it important to expand parentheses first when solving equations?
4. How can dividing or multiplying by negative numbers affect the equation?
5. What methods work best for verifying the solutions?

Tip:

When solving equations, always check your solution by substituting the value back into the original equation. This ensures accuracy!