Lesson 7: Practice Problems

Problem 1

Explain how the parts of the balanced hanger compare to the parts of the equation.

$7 = 2 x + 3$

A balanced hanger diagram with 7 squares on the left and 2 circles and 3 squares on the right with the equation 7 = 2x + 3

Problem 2

Here is a hanger:

Hanger has 5 circles and rectangle labeled 2 on the left, rectangle labeled 17 on the right

Write an equation to represent the hanger.
Draw more hangers to show each step you would take to find $x$ . Explain your reasoning.
Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.

Problem 3 From Unit 3 Lesson 3

Clare drew this diagram to match the equation $2 x + 16 = 50$ , 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.

What value for $x$ can be found using the diagram?
Show how to fix Clare’s diagram to correctly match the equation.
Use the new diagram to find a correct value for $x$ .
Explain the mistake Clare made when she drew her diagram.