# Lesson 5

Reasoning about Equations and Tape Diagrams (Part 2)

Let’s use tape diagrams to help answer questions about situations where the equation has parentheses.

### Problem 1

Here are two stories:

- A family buys 6 tickets to a show. They also
*each*spend $3 on a snack. They spend $24 on the show.

- Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Here are two equations:

- \(3(x+6)=24\)
- \(6(x+3)=24\)

- Which equation represents which story?
- What does \(x\) represent in each equation?
- Find the solution to each equation. Explain or show your reasoning.
- What does each solution tell you about its situation?

### Problem 2

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.

\(\displaystyle 6(x+1)=24\)

### Problem 3

Find a sequence of rotations, reflections, translations, and dilations showing that one figure is similar to the other. Be specific: give the amount and direction of a translation, a line of reflection, the center and angle of a rotation, and the center and scale factor of a dilation.

### Problem 4

Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scaled copies of one another? Explain.