Final answer:
The problem involves solving for the value of a matching pair in points (X), given Elena's and Karen's scores and the number of pairs they collect. The equation 2 + 3X = -6 + 4X leads to finding that X, the value of a matching pair, is 8 points.
Step-by-step explanation:
The student is asking about a card game where players Elena and Karen earn points by collecting pairs of matching cards. They start with Elena having 2 points and Karen having -6 points. After Elena collects 3 pairs and Karen collects 4 pairs, they have the same number of points.
To find the value of a matching pair in points (denoted by X), we need to set up an equation that represents the situation:
Elena's score after collecting pairs: 2 + 3X
Karen's score after collecting pairs: -6 + 4X
Since their scores are equal after collecting the pairs, we can set these expressions equal to each other:
2 + 3X = -6 + 4X.
Next, we solve for X:
2 + 3X - 4X = -6
2 - X = -6
-X = -8 (Subtract 2 from both sides)
X = 8 (Multiply both sides by -1)
Therefore, regardless of the given values for X in the question, the actual value of a matching pair in points is 8 points.