The image shows a question in German that provides three mathematical statements, and you are asked to select which ones are correct. The question involves real numbers $a$, $b$, and $c$. Let's break down each statement:

1. Statement 1: $a < b \Rightarrow -a < -b$

   • This is incorrect. If $a < b$, negating both sides reverses the inequality, meaning $-a > -b$, not $-a < -b$.

2. Statement 2: The inequality $a - 3 < 1$ has the solution set $L = (4, \infty)$.

   • Let's solve the inequality: $a - 3 < 1$ Add 3 to both sides: $a < 4$ The correct solution set should be $(-\infty, 4)$, not $(4, \infty)$. So this statement is incorrect as well.

3. Statement 3: $a < b \Rightarrow a + c < b + c$

   • This is correct. Adding the same number $c$ to both sides of the inequality does not change the inequality's direction. Therefore, $a + c < b + c$ holds true.

Conclusion:

• The only correct statement is the third one: $a < b \Rightarrow a + c < b + c$.

Do you want further details on any part of the explanation?

Here are 5 related questions:

1. What happens when we multiply or divide both sides of an inequality by a negative number?
2. How does shifting an inequality by adding or subtracting the same value affect it?
3. Can we apply similar rules for inequalities in non-real number systems (e.g., complex numbers)?
4. How can you verify if an inequality solution is correct by graphing it?
5. What are the differences between strict inequalities (e.g., $<$) and non-strict inequalities (e.g., $\leq$)?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.