# Lesson 3

Reasoning about Equations with Tape Diagrams

### Problem 1

Solve each equation mentally.

1. $$2x = 10$$
2. $$\text-3x = 21$$
3. $$\frac13 x = 6$$
4. $$\text-\frac12x = \text-7$$

### Solution

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(From Unit 5, Lesson 15.)

### Problem 2

Complete the magic squares so that the sum of each row, each column, and each diagonal in a grid are all equal.​

### Solution

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(From Unit 5, Lesson 3.)

### Problem 3

Draw a tape diagram to match each equation.

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

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

### Solution

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### Problem 4

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:

$$35-8=6x$$

### Solution

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### Problem 5

Each car is traveling at a constant speed. Find the number of miles each car travels in 1 hour at the given rate.

1. 135 miles in 3 hours

2. 22 miles in $$\frac12$$ hour

3. 7.5 miles in $$\frac14$$ hour

4. $$\frac{100}{3}$$ miles in $$\frac23$$ hour

5. $$97\frac12$$ miles in $$\frac32$$ hour

### Solution

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(From Unit 4, Lesson 2.)