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### Problem 3 (Hanger Diagram for $2b = 4$)
# Explanation:
## Step1: Analyze the hanger diagram
The left side has 2 circles labeled $b$, and the right side has 4 squares labeled 1. The hanger is balanced, so $2b = 4$.
## Step2: Solve for $b$
To find $b$, we divide both sides of the equation $2b = 4$ by 2.
$b=\frac{4}{2}$
## Step3: Calculate the value
$\frac{4}{2}=2$
# Answer:
The value of $b$ is $2$ because when we divide the total value on the right (4) by the number of $b$s on the left (2), we get $b = 2$.

### Problem 4 (Hanger Diagram for $2b + 2 = 6$)
#### Part (a)
# Brief Explanations:
To have only variables on the left, we remove the non - variable (constant) terms from both sides. The left side has 2 $b$s and 2 ones, the right side has 6 ones. We can remove 2 ones from both sides (since the hanger is balanced, removing equal amounts from both sides keeps it balanced).
# Answer:
We can remove 2 squares (each representing 1) from both sides of the hanger diagram.

#### Part (b)
# Explanation:
## Step1: Start with the original equation
The original equation from the hanger is $2b + 2=6$.
## Step2: Apply the operation from part (a)
After removing 2 ones from both sides, the left side becomes $2b$ (since we removed 2 ones from $2b + 2$) and the right side becomes $6 - 2$.
$6-2 = 4$, so the equation is $2b=4$
# Answer:
$4$

#### Part (c)
# Brief Explanations:
After getting $2b = 4$ (from part b), we can think of the hanger. The left has 2 $b$s and the right has 4 ones. To find the value of one $b$, we can split the 4 ones into two equal groups (since there are 2 $b$s). Each group will have the same number of ones as the value of one $b$.
# Answer:
We can split the 4 ones on the right side into two equal groups (because there are 2 $b$s on the left). Each group will have 2 ones, so $b = 2$.

#### Part (d)
# Explanation:
## Step1: From part (b), we have $2b = 4$
## Step2: Solve for $b$
Divide both sides of $2b = 4$ by 2. $b=\frac{4}{2}$
## Step3: Calculate the value
$\frac{4}{2}=2$
# Answer:
The value of $b$ is $2$ (found by dividing the 4 ones on the right into two equal parts, each part is 2, so $b = 2$).

### Problem 5 (Equation $3y-9 = 24$)
#### Part (a)
# Explanation:
## Step1: Start with the equation $3y-9 = 24$
## Step2: To find $3y$, we add 9 to both sides of the equation (using the addition property of equality: if $a=b$, then $a + c=b + c$)
$3y-9 + 9=24 + 9$
## Step3: Simplify the equation
$3y=33$
So we know $3y = 33$ because when we add 9 to both sides of the equation $3y-9 = 24$ to isolate $3y$, we get $3y=33$.
# Answer:
We know $3y = 33$ is true because we add 9 to both sides of the equation $3y - 9=24$ (by the addition property of equality), and $24+9 = 33$, so $3y=33$.

#### Part (b)
# Explanation:
## Step1: Start with the equation $3y = 33$ (from part a)
## Step2: To find $y$, we divide both sides of the equation by 3 (using the division property of equality: if $a = b$, then $\frac{a}{c}=\frac{b}{c}$ for $c
eq0$)
$y=\frac{33}{3}$
## Step3: Calculate the value
$\frac{33}{3}=11$
So we know $y = 11$ because when we divide both sides of the equation $3y = 33$ by 3, we get $y = 11$.
# Answer:
We know $y = 11$ is true because we divide both sides of the equation $3y = 33$ by 3 (by the division property of equality), and $\frac{33}{3}=11$, so $y = 11$.

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QUESTION IMAGE

Question

Explanation:

Problem 3 (Hanger Diagram for \(2b = 4\))

Step1: Analyze the hanger diagram

Step2: Solve for \(b\)

Step3: Calculate the value

Step1: Start with the original equation

Step2: Apply the operation from part (a)

Answer:

Problem 4 (Hanger Diagram for \(2b + 2 = 6\))

Part (a)