Let's break down the given information step by step.
We have:
- \( a = 3b + 20 \)
- \( b \) is an even integer.
Since \( b \) is an even integer, it can be expressed in the form \( b = 2k \) where \( k \) is an integer.
Substituting \( b = 2k \) into the equation for \( a \):
\[ a = 3(2k) + 20 = 6k + 20 \]
Now we have both \( a \) and \( b \) expressed in terms of \( k \):
- \( a = 6k + 20 \)
- \( b = 2k \)
Next, we can analyze their properties:
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Both \( a \) and \( b \) are integers: Since both \( k \) and the operations performed on \( k \) (multiplication and addition) yield integers, \( a \) and \( b \) are integers.
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Parity:
- \( b \) is even by definition.
- For \( a = 6k + 20 \):
- Both \( 6k \) and \( 20 \) are even, so the sum \( 6k + 20 \) is also even.
- Thus, both \( a \) and \( b \) are even integers.
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Relationship:
- Since \( a = 3b + 20 \), \( a \) is always 20 units greater than three times \( b \). This means \( a \) will always be larger than \( b \) for any positive \( b \).
In conclusion, the following can be stated:
- Both \( a \) and \( b \) are even integers.
- \( a \) is always greater than \( b \) (unless \( b \) is sufficiently negative such that the equation results in a negative \( a \)).
- The specific operations you can perform are addition, subtraction, and multiplication, with results that will always maintain the even nature.
Is there anything specific you would like to know or explore further?