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The image you've uploaded contains exercises on first-degree inequalities with one variable, and it instructs to solve only the even-numbered problems. I'll follow the instructions and solve the even-numbered inequalities.

Let's proceed:

### 2) \( 12x < 6 \)
Solve for \( x \):
\[
x < \frac{6}{12}
\]
\[
x < \frac{1}{2}
\]
**Solution**: \( x < \frac{1}{2} \)

---

### 4) \( 4 - 2x < 15 \)
1. Subtract 4 from both sides:
\[
-2x < 15 - 4
\]
\[
-2x < 11
\]
2. Divide by \(-2\) (reverse the inequality):
\[
x > -\frac{11}{2}
\]
**Solution**: \( x > -\frac{11}{2} \)

---

### 6) \( 5x - 2(x + 3) \leq x \)
1. Expand the equation:
\[
5x - 2x - 6 \leq x
\]
\[
3x - 6 \leq x
\]
2. Subtract \( x \) from both sides:
\[
2x - 6 \leq 0
\]
3. Add 6 to both sides:
\[
2x \leq 6
\]
4. Divide by 2:
\[
x \leq 3
\]
**Solution**: \( x \leq 3 \)

---

### 8) \( \frac{3}{4} x - 1 \leq \frac{1}{2} x + 2 \)
1. Multiply the entire inequality by 4 to eliminate denominators:
\[
3x - 4 \leq 2x + 8
\]
2. Subtract \( 2x \) from both sides:
\[
x - 4 \leq 8
\]
3. Add 4 to both sides:
\[
x \leq 12
\]
**Solution**: \( x \leq 12 \)

---

### 10) \( (x - 1)^2 - 7 > (x - 2)^2 \)
1. Expand both sides:
\[
(x^2 - 2x + 1) - 7 > (x^2 - 4x + 4)
\]
\[
x^2 - 2x - 6 > x^2 - 4x + 4
\]
2. Subtract \( x^2 \) from both sides:
\[
-2x - 6 > -4x + 4
\]
3. Add \( 4x \) to both sides:
\[
2x - 6 > 4
\]
4. Add 6 to both sides:
\[
2x > 10
\]
5. Divide by 2:
\[
x > 5
\]
**Solution**: \( x > 5 \)

---

This covers the even-numbered exercises as instructed. Do you want details on these solutions or have any further questions?

Here are 5 related questions to expand the discussion:
1. How do we handle inequalities when dividing by negative numbers?
2. What are the differences between solving inequalities and equalities?
3. How can inequalities be represented graphically on a number line?
4. How do compound inequalities differ from single inequalities?
5. What role do parentheses and exponents play in inequality transformations?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Realizar los ejercicios pares de las inequaciones de primer grado con una incógnita.

This set of exercises covers first-degree inequalities with one variable. Detailed solutions for even-numbered problems include using algebraic manipulation, handling inequality reversals when dividing by negative numbers, and applying the distributive property.

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