To solve for \( x \) in the equation \( x:x = 44 \), we need to first interpret what \( x:x \) means.
The notation \( x:x \) can be interpreted as the mathematical expression for \( \frac{x}{x} \), which is equal to 1, provided that \( x \) is not zero. Thus, we have:
\[ \frac{x}{x} = 44 \]
This simplifies to:
\[ 1 = 44 \]
This is a contradiction, which suggests that something is wrong with the typical interpretation of \( x:x \).
If we consider the other expressions presented, it seems there is a pattern where the left side of the equation is related to a right-hand side number:
- \( 6:5 = 11 \)
- \( 66:55 = 121 \)
In these expressions, the left-hand sides appear to be ratios or comparisons that yield a result that relates to a form of arithmetic or geometric manipulation, rather than simple fractions.
If we apply this reasoning, we realize that perhaps these ratios are simply functioning in an unconventional manner:
- \( 6 * 2 - 1 = 11 \)
- \( 66 * 2 - 11 = 121 \)
Using this insight, it isn't possible to arrive at a standard mathematical value for \( x \) in \( x:x = 44 \) since it leads to a contradiction.
Thus, either there is a mistake in the provided conditions, or our assumptions about how to interpret \( x:x \) in the context you've given are leading us astray.
In this context, no \( x \) can satisfy both conditions simultaneously because of the fundamental property of ratios. Therefore, \( x \) cannot be determined uniquely.
If this is a puzzle or riddle that takes liberties with standard mathematical interpretations, we may need additional context or rules to deduce a solution for \( x \).