Question

4 the hanger diagram models $2b \div 2 = 6$. you can use this diagram to find the value of $b$.
a. what can you remove from both 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.
$2b = \underline{\quad}$
c. how can you use the diagram to find the value of $b$?
d. what does the diagram show is the value of $b$?
5 think about the equation $3y - 9 = 24$.
a. the value of $3y$ is 33. how do you know this is true?
b. the value of $y$ is 11. how do you know this is true?

Explanation:

Step1: Remove 2 from both sides

Original equation: $2b + 2 = 6$
Subtract 2 from both sides: $2b + 2 - 2 = 6 - 2$

Step2: Simplify to get new equation

Simplify the expression: $2b = 4$

Step3: Isolate b by dividing by 2

Divide both sides by 2: $\frac{2b}{2} = \frac{4}{2}$

Step4: Simplify to find b

Simplify the expression: $b = 2$

Step5: Verify 3y = 33

Original equation: $3y - 9 = 24$
Add 9 to both sides: $3y - 9 + 9 = 24 + 9$
Simplify: $3y = 33$

Step6: Verify y = 11

Divide both sides by 3: $\frac{3y}{3} = \frac{33}{3}$
Simplify: $y = 11$

Answer:

For Question 4:

a. Remove the two blocks labeled "1" from each side (the two crossed blocks on the left, and two matching "1" blocks on the right).
b. $2b = 4$
c. Split the remaining blocks on both sides into two equal groups (each group has one $b$ on the left and two "1" blocks on the right).
d. $b = 2$

For Question 5:

a. Add 9 to both sides of $3y - 9 = 24$, so $3y = 24 + 9 = 33$.
b. Divide both sides of $3y = 33$ by 3, so $y = \frac{33}{3} = 11$.