Question

write an equation that represents the weights on the hanger.

Explanation:

Step1: Analyze left side weights

The left side has 2 \(a\) weights and 1 weight of 1, so total weight is \(2a + 1\).

Step2: Analyze right side weights

Count the number of 1 - unit weights on the right. There are 5 + 4 = 9? Wait, no, looking at the hanger: left has two \(a\) and one 1. Right: first column 5 ones, second column 4 ones? Wait, no, the image: left side: two \(a\) (top two) and one 1 (bottom). Right side: first vertical stack: 5 ones (since from top to bottom, 5 blocks each labeled 1), second vertical stack: 4 ones? Wait, no, let's count again. Wait, the left: two \(a\) and one 1, so \(2a + 1\). The right: let's count the number of 1s. First stack (left - most on right): 5? Wait, no, the right side has two stacks? Wait, the hanger is balanced, so left weight equals right weight. Looking at the numbers given (2, a, 1, 9). So left: \(2a+1\), right: 9? Wait, 2a + 1 = 9? Wait, let's check: two \(a\)s and one 1 on left. On right, how many 1s? Let's count the blocks: first column (right of the center) has 5 blocks (1,1,1,1,1) and second column has 4 blocks (1,1,1,1)? Wait, no, 5 + 4 = 9. So left: 2a + 1, right: 9. So equation is \(2a + 1 = 9\).

Answer:

\(2a + 1 = 9\)