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The image contains a mathematical example from the context of inductive reasoning:

**Example 3:**
1. Pick a number.
2. Multiply the number by 4.
3. Add 8 to the product.
4. Divide the sum by 2.
5. Subtract 5.

After completing this procedure for several numbers, use inductive reasoning to make a conjecture about the relationship between the size of the resulting number and the size of the original number.

### Solution Outline:
Let's define the original number as \( x \).

Following the steps:
1. Multiply by 4: \( 4x \)
2. Add 8: \( 4x + 8 \)
3. Divide by 2: \( \frac{4x + 8}{2} = 2x + 4 \)
4. Subtract 5: \( (2x + 4) - 5 = 2x - 1 \)

So, after performing the operations, the final result is \( 2x - 1 \).

### Conjecture:
The size of the resulting number is related to the original number in a linear fashion: it is **double** the size of the original number minus 1.

Would you like further explanation or examples? Here are five related questions for further exploration:

1. What happens if the original number is negative or zero?
2. How does this pattern compare to other linear functions?
3. Can we reverse the process to find the original number given the result?
4. What changes if we modify the constants in the process?
5. How can we visualize this relationship on a graph?

**Tip:** Inductive reasoning involves identifying patterns based on examples, which is different from deductive reasoning that starts with general rules.

Consider the following. Pick a number. Multiply the number by 4, add 8 to the product, divide the sum by 2, and subtract 5. Complete the above procedure for several different numbers. Use inductive reasoning to make a conjecture about the relationship between the size of the resulting number and the size of the original number.

Explore an example of inductive reasoning through an algebraic process involving multiplication, addition, division, and subtraction. Learn how to analyze patterns and make conjectures about the relationship between the original number and the resulting number. Suitable for Grades 8-10.

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