# Lesson 3

Reasoning about Equations with Tape Diagrams

### Problem 1

Draw a tape diagram to match each equation.

1. $$5(x+1)=20$$

2. $$5x+1=20$$

### Problem 2

Select all the equations that match the tape diagram.

A:

$$35=8+x+x+x+x+x+x$$

B:

$$35=8+6x$$

C:

$$6+8x=35$$

D:

$$6x+8=35$$

E:

$$6x+8x=35x$$

F:

$$35-8=6x$$

### Problem 3

Point $$B$$ has coordinates $$(\text-2,\text-5)$$. After a translation 4 units down, a reflection across the $$y$$-axis, and a translation 6 units up, what are the coordinates of the image?

### Solution

(From Unit 1, Lesson 5.)

### Problem 4

Figure 2 is a scaled copy of Figure 1.

1. Identify the points in Figure 2 that correspond to the points $$A$$ and $$C$$ in Figure 1. Label them $$P$$ and $$R$$. What is the distance between $$P$$ and $$R$$?
2. Identify the points in Figure 1 that correspond to the points $$Q$$ and $$S$$ in Figure 2. Label them $$B$$ and $$D$$. What is the distance between $$B$$ and $$D$$?
3. What is the scale factor that takes Figure 1 to Figure 2?
4. $$G$$ and $$H$$ are two points on Figure 1, but they are not shown. The distance between $$G$$ and $$H$$ is 1. What is the distance between the corresponding points on Figure 2?