Solve for \[x\].
Assume the equation has a solution for \[x\].
\[n\cdot(17+x) = 34x-r\]

To solve the equation for \( x \):

\[
n \cdot (17 + x) = 34x - r
\]

First, distribute \( n \) on the left side:

\[
n \cdot 17 + n \cdot x = 34x - r
\]

This simplifies to:

\[
17n + nx = 34x - r
\]

Next, get all terms involving \( x \) on one side of the equation and the constant terms on the other:

\[
nx - 34x = -r - 17n
\]

Factor out \( x \) on the left side:

\[
x(n - 34) = -r - 17n
\]

Finally, solve for \( x \) by dividing both sides by \( (n - 34) \):

\[
x = \frac{-r - 17n}{n - 34}
\]

So, the solution for \( x \) is:

\[
x = \frac{-r - 17n}{n - 34}
\]

Let me know if you need more details, have any questions, or would like to explore related problems! 

Here are 5 related questions you might find useful:
1. What happens to \( x \) if \( n = 34 \)?
2. How would the solution change if \( r = 0 \)?
3. Can you solve for \( n \) in terms of \( x \)?
4. What are the implications if \( n = 0 \)?
5. How does the value of \( r \) affect the solution for \( x \)?

**Tip:** Always check for any restrictions or conditions (like denominators being zero) when solving algebraic equations.

Learn how to solve the equation n*(17+x) = 34x - r step-by-step with detailed algebraic methods. This problem involves distributing terms, rearranging equations, and solving for x in terms of n and r. Suitable for high school students and anyone interested in algebraic equations.

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