The image contains a series of inequalities to solve over $\mathbb{R}$. Here's a transcription of the inequalities provided in the image:

Exercise 2: Solve the following inequalities in $\mathbb{R}$:

1. $(1 - \sqrt{2})x - 5 \leq 0$
2. $3x - 5 < 7 - \sqrt{2}x$
3. $\frac{7x - 2}{1 - \sqrt{3}} \leq \frac{7x + 2}{1 + \sqrt{3}}$
4. $|x - 5| < \frac{1}{2}$
5. $|x + 2| - |5| \leq 4$
6. $|3x - 2| > 3$

Would you like me to solve these one by one and provide detailed explanations for each step? If yes, please let me know if you have a preference for which inequality to start with.

Here are five related questions to consider:

1. Would you like a general explanation of solving linear inequalities?
2. Do you want assistance with absolute value inequality steps?
3. Should we work on rational inequalities first?
4. Do you need a graph or visualization of any of the solutions?
5. Do you want me to check conditions of equality or boundaries?

Tip: When solving inequalities, always consider simplifying terms and flipping the inequality sign if multiplying or dividing by a negative.