Let's go through the given procedure step by step with a few different numbers to see if we can establish a pattern.

Procedure:

1. Pick a number: $x$
2. Multiply the number by 9: $9x$
3. Add 15 to the product: $9x + 15$
4. Divide the sum by 3: $\frac{9x + 15}{3} = 3x + 5$
5. Subtract 5: $3x + 5 - 5 = 3x$

Conclusion:

After performing the procedure for any number $x$, the final result is always $3x$.

Testing the Procedure:

• If $x = 1$:
  $9 \times 1 = 9$,
  $9 + 15 = 24$,
  $\frac{24}{3} = 8$,
  $8 - 5 = 3$,
  Result: $3 \times 1 = 3$.

• If $x = 2$:
  $9 \times 2 = 18$,
  $18 + 15 = 33$,
  $\frac{33}{3} = 11$,
  $11 - 5 = 6$,
  Result: $3 \times 2 = 6$.

• If $x = 3$:
  $9 \times 3 = 27$,
  $27 + 15 = 42$,
  $\frac{42}{3} = 14$,
  $14 - 5 = 9$,
  Result: $3 \times 3 = 9$.

Conjecture:

The final result is always three times the original number. In other words, the output is directly proportional to the input, with a proportionality factor of 3.

Summary:

For any number $x$, the final result will be $3x$. This indicates that the size of the resulting number is three times the size of the original number.

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Do you want any more details or have any questions?

Here are 5 related questions to consider:

1. How would the procedure change if we doubled the original number at the start?
2. Can you modify the procedure to result in $4x$ instead of $3x$?
3. What happens if we add a constant number at a different stage in the process?
4. Can you write a generalized equation for any modification to this procedure?
5. How would the result change if we replaced multiplication by 9 with multiplication by 7?

Tip: When working with procedures, always break down each step algebraically to spot patterns or make conjectures.