**Solve for \[n\].**
*Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.*

\[64n-6 \geq 36n -16\]


Let's solve the inequality \(64n - 6 \geq 36n - 16\).

1. **Subtract \(36n\) from both sides**:
   \[
   64n - 36n - 6 \geq -16
   \]
   Simplifying this gives:
   \[
   28n - 6 \geq -16
   \]

2. **Add 6 to both sides**:
   \[
   28n - 6 + 6 \geq -16 + 6
   \]
   Simplifying this gives:
   \[
   28n \geq -10
   \]

3. **Divide both sides by 28**:
   \[
   n \geq \frac{-10}{28}
   \]
   Simplifying the fraction to its lowest terms gives:
   \[
   n \geq \frac{-5}{14}
   \]

So, the solution is:
\[
n \geq \frac{-5}{14}
\]

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How do you solve inequalities involving fractions?
2. What are the rules for multiplying or dividing both sides of an inequality by a negative number?
3. Can you explain how to solve compound inequalities?
4. What are the differences between solving an equation and an inequality?
5. How do you graph the solution to an inequality on a number line?

**Tip:** When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the inequality 64n - 6 ≥ 36n - 16 step-by-step with a detailed solution. This problem involves basic algebraic concepts and inequalities. Suitable for students in Grades 7-9.

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