3.1: Matching Hangers
Figures A, B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights
from each side.

Here are some equations. Each equation represents one of the hanger diagrams.
2(x + 3y) = 4x + 2y
2y = x
2(x + 3y) + 2z = 2z + 4x + 2y
x + 3y = 2x + y

1. Write the equation that goes with each figure:
A:
B:
C:
D:

2. Each variable (x, y, and z) represents the weight of one shape. Which goes with which?

3. Explain what was done to each equation to create the next equation. If you get stuck, think about
how the hangers changed.