Lesson 8

Reasoning about Solving Equations (Part 2)

Let’s use hangers to understand two different ways of solving equations with parentheses.

Problem 1

Here is a hanger:

  1. Write an equation to represent the hanger.
  2. Solve the equation by reasoning about the equation or the hanger. Explain your reasoning.
Hanger has 5 groups of a circle + rectangle labeled with 2 on the left, rectangle labeled with 11 on the right

Problem 2

Explain how each part of the equation \(9=3(x+2)\) is represented in the hanger.

  • \(x\)
  • 9
  • 3
  • \(x+2\)
  • \(3(x+2)\)
  • the equal sign
Balanced hanger, left side, 9 squares each labeled 1.  Right side, three groups, each group contains one circle labled x and 2 squares labeled 1.

Problem 3

Select the word from the following list that best describes each situation.

(From Unit 4, Lesson 11.)

Problem 4

Clare drew this diagram to match the equation \(2x+16=50\), but she got the wrong solution as a result of using this diagram. 

A tape diagram partitioned into three different sized rectangles, labeled 2, x and 16. The total length of the bar is labeled 50.


  1. What value for \(x\) can be found using the diagram?
  2. Show how to fix Clare’s diagram to correctly match the equation. 
  3. Use the new diagram to find a correct value for \(x\).
  4. Explain the mistake Clare made when she drew her diagram.
(From Unit 6, Lesson 3.)