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The image you provided shows a set of algebraic exercises, including inequalities and equations. I’ll address the key problems and guide you through the solutions.

### Let's break it down into different sections:

#### III. Inequalities
This section asks you to express inequalities and graph them on a number line.

1. \( x < 6 \)
   - Solution: All values less than 6 (open circle at 6).
   
2. \( -4 \leq x \leq 3 \)
   - Solution: All values between -4 and 3 (inclusive, closed circles at -4 and 3).
   
3. \( x \geq -5 \)
   - Solution: All values greater than or equal to -5 (closed circle at -5).

#### IV. Solving Equations and Answering Based on Their Solutions
This section includes solving linear equations, absolute value equations, and simple fractional equations.

1. \( 3x - 4 = x + 5 \)
   - Solution:
     \[
     3x - x = 5 + 4 \implies 2x = 9 \implies x = \frac{9}{2}
     \]

2. \( x + 2 = 5 \)
   - Solution:
     \[
     x = 5 - 2 \implies x = 3
     \]

3. \( 2x - 5 = 7 \)
   - Solution:
     \[
     2x = 7 + 5 \implies 2x = 12 \implies x = 6
     \]

4. \( x - 3 < 4x + 7 \)
   - Solution:
     \[
     -3x < 7 + 3 \implies -3x < 10 \implies x > -\frac{10}{3}
     \]
   (Remember to flip the inequality when dividing by a negative.)

5. \( x - 1 = x + 1 \)
   - Solution:
     This equation simplifies to \( 0 = 2 \), which is a contradiction. Therefore, there is **no solution**.

If you want to review more problems or explore specific ones in greater detail, feel free to ask!

### Do you need more details or have any specific questions?

### Here are 5 related questions:
1. How do you graph the solution to a compound inequality like \( -2 < x \leq 3 \)?
2. What is the process to solve absolute value equations like \( |2x - 3| = 5 \)?
3. How do you solve quadratic equations that are part of the exercise?
4. What methods can be used to solve systems of linear equations algebraically?
5. Can inequalities be solved graphically on a coordinate plane?

### Tip:
When solving inequalities, always be careful to reverse the inequality sign when multiplying or dividing both sides by a negative number!

Explore algebraic exercises involving inequalities and equations with detailed solutions. Learn to solve inequalities, graph them on a number line, and tackle various types of equations including linear and absolute value equations. Suitable for high school students.

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