# Lesson 12

Balanced Moves

### Problem 1

In this hanger, the weight of the triangle is $$x$$ and the weight of the square is $$y$$.

1. Write an equation using $$x$$ and $$y$$ to represent the hanger.

2. If $$x$$ is 6, what is $$y$$?

### Problem 2

Andre and Diego were each trying to solve $$2x+6=3x-8$$. Describe the first step they each make to the equation.

1. The result of Andre’s first step was $$\text-x+6=\text-8$$.

2. The result of Diego’s first step was $$6=x-8$$.

### Problem 3

Match each set of equations with the move that turned the first equation into the second.

### Problem 4

What is the weight of a square if a triangle weighs 4 grams?

### Problem 5

Here is a balanced hanger diagram.

Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and $$x$$ represents the weight of each square. Select all equations that represent the hanger.

A:

$$x+x+x+x+11=x+11.5$$

B:

$$2x=0.5$$

C:

$$4x+5+6=2x+2.5+6$$

D:

$$2x+2.5=3$$

E:

$$4x+2.5+2.5+3+3=2x+2.5+3+3+3$$