To find all pairs of consecutive even positive integers, both of which are greater than 10 and their sum is less than 50, we can proceed as follows:

Let the consecutive even integers be $x$ and $x + 2$.

Given:

1. Both integers are greater than 10.
2. Their sum is less than 50.

The conditions can be expressed as: $x > 10$ $x + (x + 2) < 50$

Simplify the inequality: $2x + 2 < 50$ $2x < 48$ $x < 24$

So, $x$ must satisfy: $10 < x < 24$

Since $x$ must be an even integer, the possible values for $x$ are: $12, 14, 16, 18, 20, 22$

We can now form the pairs by adding 2 to each of these values:

1. $x = 12$: The pair is (12, 14)
2. $x = 14$: The pair is (14, 16)
3. $x = 16$: The pair is (16, 18)
4. $x = 18$: The pair is (18, 20)
5. $x = 20$: The pair is (20, 22)
6. $x = 22$: The pair is (22, 24)

Thus, the pairs of consecutive even positive integers both of which are greater than 10 and whose sum is less than 50 are:

$(12, 14), (14, 16), (16, 18), (18, 20), (20, 22), (22, 24)$

Would you like any more details or have any questions?

Here are five more questions you can ask:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the process to find the derivative of a polynomial function?
3. Can you explain how to integrate by parts with an example?
4. How do you determine the limit of a function as it approaches a specific point?
5. What are the properties of definite integrals and how are they applied?

Tip: When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number.