I see there are several equations that require solving for $x$ using distribution. Let's go through each equation shown in the image.

Problem 1

Equation:
$7 + 5(x - 2) = 12$

Solution:

1. Distribute the $5$ across $(x - 2)$: $7 + 5x - 10 = 12$
2. Combine like terms on the left: $5x - 3 = 12$
3. Add $3$ to both sides: $5x = 15$
4. Divide by $5$: $x = 3$

Problem 3

Equation:
$7x + 3(4x - 8) = 109$

Solution:

1. Distribute the $3$ across $(4x - 8)$: $7x + 12x - 24 = 109$
2. Combine like terms on the left: $19x - 24 = 109$
3. Add $24$ to both sides: $19x = 133$
4. Divide by $19$: $x = 7$

Problem 5

Equation:
$-4x - 7(-3x - 6) = 195$

Solution:

1. Distribute the $-7$ across $(-3x - 6)$: $-4x + 21x + 42 = 195$
2. Combine like terms on the left: $17x + 42 = 195$
3. Subtract $42$ from both sides: $17x = 153$
4. Divide by $17$: $x = 9$

Problem 7

Equation:
$8(x + 5) + 4 = 60$

Solution:

1. Distribute the $8$ across $(x + 5)$: $8x + 40 + 4 = 60$
2. Combine like terms on the left: $8x + 44 = 60$
3. Subtract $44$ from both sides: $8x = 16$
4. Divide by $8$: $x = 2$

Let me know if you need further details on any steps or additional problems solved!

Follow-up Questions:

1. What is the distributive property and how does it work in equations?
2. How do you combine like terms in equations?
3. Why is it important to isolate the variable $x$ when solving equations?
4. What methods can be used to check solutions after solving?
5. How does one handle negative signs in distribution?

Tip:

When working with equations, always perform the same operation on both sides to maintain balance!