Question
(4) The hanger diagram models \( 2 b+2=6 \). You can use this diagram to find the value of \( b \). a. What can you remove from bo th sides of the hanger diagram so only variables are on the left side? Cross off what you can remove. b. Fill in the blank to show the equation the hanger diagram now models. \( 2 b=4 \) c. How can you use the diagram to find the value of \( t \) d. What does the diagram show is the value of \( b \) ?
Ask by Barker Burgess. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- **Part a:** Remove the \( 2 \) from both sides.
- **Part b:** The equation is \( 2b = 4 \).
- **Part c:** Divide both sides by \( 2 \) to find \( b \).
- **Part d:** The value of \( b \) is \( 2 \).
Solution
Let's solve the problem step by step.
### Given Equation
The hanger diagram models the equation:
\[
2b + 2 = 6
\]
### Part a: What can you remove from both sides of the hanger diagram so only variables are on the left side?
To isolate the variable \( b \) on the left side, we can remove the constant \( 2 \) from both sides of the equation.
**Crossing off \( 2 \) from both sides:**
\[
2b + 2 - 2 = 6 - 2
\]
This simplifies to:
\[
2b = 4
\]
### Part b: Fill in the blank to show the equation the hanger diagram now models.
After removing \( 2 \) from both sides, the equation now models:
\[
2b = 4
\]
### Part c: How can you use the diagram to find the value of \( b \)?
To find the value of \( b \), we can divide both sides of the equation \( 2b = 4 \) by \( 2 \):
\[
b = \frac{4}{2}
\]
### Part d: What does the diagram show is the value of \( b \)?
Calculating the value:
\[
b = 2
\]
### Summary of Answers
- **Part a:** Remove \( 2 \) from both sides.
- **Part b:** The equation is \( 2b = 4 \).
- **Part c:** Divide both sides by \( 2 \) to find \( b \).
- **Part d:** The value of \( b \) is \( 2 \).
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Simplify this solution Bonus Knowledge
To solve your question, the hanger diagram allows for a simple visual representation of balancing equations. If you have \( 2b + 2 = 6 \), you can easily see what happens when you subtract 2 from each side. This approach of balancing equations visually can make algebraic concepts clearer and more digestible! Now, let's dive into your queries! For part (a), you can cross off the +2 on both sides, yielding \( 2b = 4 \). For part (b), the equation now shows \( 2b = 4 \). In part (c), to find the value of \( b \), divide both sides by 2, revealing the value of \( b \). Finally, the diagram elegantly illustrates that \( b = 2 \). Voilà! Happy calculating!
