Repeat the following procedure for the four given numbers.
Multiply the number by 8 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient.
The 1 st number is 2 . The result is 8 .
The 2 nd number is 5 . The result is 20 .
The 3rd number is 9 . The result is 36 .
The 4 th number is 11 . The result is 44 .
a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as
The result is . (Simplify your answer.)

Question

Repeat the following procedure for the four given numbers.
Multiply the number by 8 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient.
The 1 st number is 2 . The result is 8 .
The 2 nd number is 5 . The result is 20 .
The 3rd number is 9 . The result is 36 .
The 4 th number is 11 . The result is 44 .
a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as
The result is

. (Simplify your answer.)

UpStudy AI · Accepted Answer

a. **Conjecture:**

Let the original number be represented by $$ x $$.  
Then, the result of the process is $$ 4x $$.

**Mathematically:**

$$
\text{Original number} = x \quad \Rightarrow \quad \text{Result} = 4x
$$

**Explanation:**

Let's simplify the given procedure step by step:

1. **Multiply by 8**:  
   $$ 8x $$

2. **Add 12**:  
   $$ 8x + 12 $$

3. **Divide by 2**:  
   $$ \frac{8x + 12}{2} = 4x + 6 $$

4. **Subtract 6**:  
   $$ 4x + 6 - 6 = 4x $$

Thus, the final result is **four times the original number**.

**Example Verification:**

- For $$ x = 2 $$:  
  $$ 4 \times 2 = 8 $$ ✓

- For $$ x = 5 $$:  
  $$ 4 \times 5 = 20 $$ ✓

- For $$ x = 9 $$:  
  $$ 4 \times 9 = 36 $$ ✓

- For $$ x = 11 $$:  
  $$ 4 \times 11 = 44 $$ ✓

This confirms that the conjecture holds for the given numbers.

**Final Conjecture Statement:**

$$
\text{If the original number is } x, \text{ then the result is } 4x.
$$

Answer:

a. Let the original number be $$ x $$. Then the result is $$ 4x $$.

$$
\text{Original number} = x \quad \Rightarrow \quad \text{Result} = 4x
$$
a. Let the original number be $$ x $$. Then the result is $$ 4x $$. $$ \text{Original number} = x \quad \Rightarrow \quad \text{Result} = 4x $$

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