# Let n be the number used for the given number puzzle. Use algebra to show how the puzzle works. ...

## Question:

Let {eq}n {/eq} be the number used for the given number puzzle. Use algebra to show how the puzzle works.

1. Pick a number

2. Subtract 9

3. Multiply by 6

4. Divide by 3

6. Subtract twice the original number.

## Algebraic Expressions:

Algebraic expressions are mathematical translations of English. Each operation has words that are used to describe it. For example, "addition" can be described as "sum", "together", and "plus".

As given in the problem, let {eq}n {/eq} be the number. Translate each step of the problem as an operation to build an algebraic expression.

1. Pick a number: {eq}n {/eq}

2. Subtract 9: {eq}n - 9 {/eq}

3. Multiply by 6: {eq}6(n-9) {/eq}

4. Divide by 3: {eq}\frac{6(n-9)}{3} {/eq}

5. Add 18: {eq}\frac{6(n-9)}{3} + 18 {/eq}

6. Subtract twice the original number: {eq}\frac{6(n-9)}{3} + 18 - 2n {/eq}

Now simplify the algebraic expression.

{eq}\begin{aligned} \frac{6(n-9)}{3}+18 - 2n \quad &\implies \quad \frac{3\cdot 2(n-9)}{3} + 18 -2n\\ &\implies \quad 2(n-9) + 18 -2n\\ &\implies \quad 2n-18 + 18 -2n\\ &\implies \quad 0\\ \end{aligned} {/eq}