To balance the hanger, we need to distribute the weights such that both sides have equal total weight. In this case, we have two labeled weights: 2 grams and 9 grams.
Let's call the weight of each circle "x" grams.
On the left side, we have one circle and one labeled weight:
Total weight on the left side = x grams + 2 grams
On the right side, we have one circle and one labeled weight:
Total weight on the right side = x grams + 9 grams
For the hanger to be balanced, the total weight on the left side must equal the total weight on the right side. So we can set up an equation:
x grams + 2 grams = x grams + 9 grams
Now, we can solve for x:
2 grams = 9 grams
To balance the hanger, each circle must weigh 2 grams.